Answer: The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Plugging in the given coordinates, the area of the triangle is:
A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))
A = 1/2(-3)(-2)+(-2)(3)+1(-3)
A = -9+6-3
A = 4
Step-by-step explanation: Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).
Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).
Step 4: Solve the equation: A = -9+6-3.
Step 5: Find the area of the triangle: A = 4.
Suppose that 8∫3 f(x)dx=6 and 8∫3 g(x)dx=-2 Which of the following is NOT necessarily true?
The correct derivative expressions of the given ones are -
[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]
[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]
[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.It is given that -
[tex]$\int\limits^3_8 {f(x)} \, dx = 6\\[/tex]
and
[tex]$\int\limits^3_8 {g(x)} \, dx[/tex]
The correct statements of the given are -
[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]
[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]
[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]
Therefore, the correct derivative expressions of the given ones are -
[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]
[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]
[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]
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Answer:
C. ∫(f·g)dx = -12 is incorrect
Step-by-step explanation:
You want to know which of the integral expressions is incorrect given ...
[tex]\displaystyle \int_3^8{f(x)}\,dx=6\ \ \text{ and }\int_3^8{g(x)}\,dx=-2[/tex]
LimitsExpression A has the same value for upper and lower limits of the integral. The area being integrated has zero width, so its value will be zero, as shown in expression A.
Expression E has the limits reversed from those in expression B, so the value of that integral will be the opposite of the value shown for B. Both of these integral expressions (B, E) are correct.
SumsThe integral of a sum is the sum of the integrals. This is shown in expressions B, D, and E, all of which are correct.
ProductIn general, the integral of a product will have no relation to the product of integrals. Hence expression C is NOT necessarily correct.
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In a density curve, proportion of data is represented by O area above the curve. O area under the curve. O the shape of the curve. o intervals of values on the vertical axis. o intervals of values on the horizontal axis. O the length of the curve
In a density curve, the proportion of data is represented by the area under the curve.
Therefore the answer is "area under the curve".
The area under the curve represents the probability or proportion of data within a certain interval. The curve itself represents the distribution of the data and the shape of the curve provides information about the type of distribution (e.g. normal, skew, etc.).
The intervals on both the horizontal and vertical axis are used to measure the density of the data, but they do not represent the proportion of data themselves. The length of the curve has no significance in representing the proportion of data.
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At your floral business, you can sell 400 bouquets for a total benefit of $4,800. If you
earn $7,200 when selling 600 bouquets, what is your marginal benefit in this range?
The marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.
How to find the marginal benefitTo find the marginal benefit in this range, we need to calculate the additional benefit of selling one more bouquet within this range.
First, let's find the benefit per bouquet in the range between selling 400 and 600 bouquets:
Total benefit in the range = $7,200 - $4,800 = $2,400
Number of bouquets in the range = 600 - 400 = 200
Benefit per bouquet in the range = Total benefit / Number of bouquets = $2,400 / 200 = $12
So for each bouquet sold within the range between 400 and 600, the benefit is $12.
Therefore, the marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.
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Please help quickly! These triangles are similar. PR=___ units
Based on the definition of similar triangles, the length of PR is 16 units.
What are the Sides of Similar Triangles?In similar triangles, corresponding sides are in proportion. This means that if two triangles are similar, their corresponding sides will have the same ratio.
Therefore, we will have the proportion:
8/6 = (x + 7 + x - 1) / (x + 7)
4/3 = (2x + 6) / (x + 7)
Cross multiply:
3(2x + 6) = 4(x + 7)
6x + 18 = 4x + 28
6x - 4x = -18 + 28
2x = 10
x = 5
PR = x + 7 + x - 1
PR = 2x + 6 = 2(5) + 6
PR = 16 units
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What is the measurement of AB?
I will give brainiest to whoever answers it right.
The measurement of AB is given as follows:
AB = 16.23.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For the angle of 52º, we have that:
AB is the hypotenuse.10 is the length of the adjacent side.Hence the measurement of AB is obtained as follows:
cos(52º) = 10/AB
AB = 10/cos(52º)
AB = 10/0.616
AB = 16.23.
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Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
What is P(AAssume that we have two
events, A and&nbB)?
What is P(A | B)?
Is P(A | B) equal to P(A)?
Are events A and B dependent or independent?
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
a) The value of P(A∩B) = 0.
b) The value of P(A|B) = 0.
c) P(A|B) is not equal to P(A). A and B are independent events.
d) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.
e) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.
a) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.
b) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.
c) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.
However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).
d) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.
If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.
e) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.
Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.
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Complete question is:
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
a) What is P(A∩B)?
b) What is P(A | B)?
c) Is P(A | B) equal to P(A)?
Are events A and B dependent or independent?
d) A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
e) What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
picture below........
The area of the given figure above can be calculated through the addition of the area of a rectangule and the area of a trapezium would be = 110km²
How to calculate the area of the given figure?The area of the rectangle= length× width
where length = 17km
width = 4km
area = 17×4= 68km²'&&&&&&
The area of trapezium; = ½(a+b)h
where a= 12 km
B= 17-12 = 5 km
h = 3+4 = 7 km
area = ½(5+7)×7
= ½× 12×7
= 6×7 = 42km²
Therefore the area of the figure = 68+42 = 110km²
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If you horizontally stretch the quadratic parent function f(x)=x^2 by a factor of 4.
When you horizontally stretch the parent function f(x)=x² by a factor of 4, the new function becomes f(x)= (1/4) x².
The function can be stretched or shrunk in different directions to produce new functions that are similar in shape but differ in size and orientation.
When you horizontally stretch the function f(x)=x² by a factor of 4, the function becomes
=> f(x)= (1/4) x².
To understand this, let's look at the equation of the parent function in detail.
The equation of the parent function f(x)=x² can be written as
=> y=x².
The x values represent the horizontal distances from the origin, and the y values represent the vertical distances from the origin.
When you stretch the function horizontally by a factor of 4, it means that the x values will be multiplied by 4. In other words, the distance from the origin in the x direction will be four times larger. The new equation of the stretched function will be
=> y= (1/4) (4x)².
We can simplify this equation to y= (1/4) x².
In mathematical terms, the horizontal stretching of a function is equivalent to multiplying the independent variable (x) by a constant factor. In this case, the constant factor is 1/4. The constant factor of 1/4 in the equation
=> y= (1/4) x²
represents the horizontal stretch by a factor of 4. The effect of this horizontal stretch is that the parabolic shape of the function will be wider and flatter compared to the parent function. The shape of the parabolic graph of the stretched function will be similar to the parent function, but the x values will be multiplied by 4.
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Exponents please help me!
Answer:
Step-by-step explanation:
(5/3)[tex]d^{3}[/tex]*(-1/3)[tex]x^{3}[/tex]=(-5/9)[tex]d^{3} x^{3}[/tex]
Find the value of x
The value of the angles x is 121 degrees
How to determine the value of the variable
It is important to note that the sum of interior angles of a polygon takes the expression
(n -2) 180
Then, we have;
(6-2) 180
720
Then, add all the angles and equate to 720. we get;
105 + 88 + 142 + 140 + 124 + x = 720
Add the values
599 + x = 720
Collect the like terms
x = 720 - 599
x = 121 degrees
Hence, the value is 121 degrees
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A student traveled at an average distance of 8 miles in 16 minutes. Which of the following relationships represent the situation between the time, t, and the total distance traveled, d?
Answer: You would be going 30 miles per hour if you traveled 8 miles in 16 minutes
Step-by-step explanation:
How long does it take for $250 to grow to $600 at 4% annual percentage rate compounded continuously? Round to
the nearest year.
Answer:
22yrs
Step-by-step explanation:
So, the money will grow to $600 in about$$ 22 years.
select all the possible solutions of 20y> -5 + 18y
Answer:
Step-by-step explanation:
2y>-5
y>-2.5
An aerial photograph is taken of a building. The photograph is made when the angle of elevation of the sun is 24 degrees. The shadow is determined to be 60 feet long. How tall is the building?
Answer:
36
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!
Which of the following inequalities does the graph represent?
Answer:
- 1/2< x ≤ 3
Step-by-step explanation:
The filled circle (at point 3) indicates that 3 is included in the inequality and the clear circle at -1/2 indicates that -1/2 is not included
Find the explicit equation.
Answer:
f(n) = 23-5n
Step-by-step explanation:
The initial number everywhere is always 23, so that's the start number. Than for every "n" it subtracts 5.
According to the U. S. Mint, the number of quarters minted in 2018 was about 2 x 10°. The mass of a quarter is about 6 X 10-3 kg. Write the number of quarters and the mass of a quarter in standard form
The number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg
About the massThe number of quarters minted in 2018 is 2 x 10°, which in standard form is simply 2. The mass of a quarter is 6 x 10^-3 kg, which in standard form is 0.006 kg. So, the number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg
A unit of mass is a unit used to measure mass. Mass is a physical property of an object that is used to explain various observed object behaviors.
In everyday life, mass is always synonymous with weight. But in reality, mass and weight are different. The weight is caused by the interaction between the mass and the Earth's gravitational field.
For example, an object with a weight on earth, when it is sent into outer space or to another planet, the object has no weight because there is no gravity. However, the object still has the same mass.
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The sum of 3 consecutive even numbers is 102 what numbers are these?
ANSWER :
hope it helped
ExPLANATION:
In linear regression, one variable, called a __________ variable, is related to one or more ____________ variables by a linear equation.
A. dependent; response
B. independent; dependent
C. response; dependent
D. dependent; independent
In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.
What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).
In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.
That is, the input of the function is the independent variable and the output is the dependent variable.
In the case of multiple inputs, all the inputs are independent variables.
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*NEED HELP COMPLETING THIS*
Simplify all radicals using the Perfect Square/Cube Factors Method as demonstrated in class.
The answers to all parts shown below.
What is Radical?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol.
Given:
We have to find the Square/Cube Factors
1. 5/6√3
Now, rationalizing
5/6√3 x √3/ √3
= 5√3 / 18
2. √3/ (7- 3√5)
Now, rationalizing
= √3/ (7- 3√5) x (7+ 3√5) / (7+ 3√5)
= √3(7+ 3√5) / 4
3. 8/ (4 + 5√2)
Now, rationalizing
= 8/ (4 + 5√2) x (4 - 5√2)/ (4 - 5√2)
= -8 (4 - 5√2)/ 34
4. 7 ∛(48 [tex]m^{18} n^{13}[/tex])
= 14 [tex]m^6[/tex][tex]n^4[/tex]∛6n
5.[tex]2\sqrt{\left(-300x^{18}\right)}[/tex]
=[tex]20\sqrt{3}\sqrt{-x^{18}}[/tex]
6. (4+ 7√10)²
= 4² + (7√10)²+ 2 (4)( 7√10)
= 16 + 490 + 56√10
= 506 + 56√10
7. (6- 7√3) x (6+ 7√3)
= 6² - (7√3)²
= 36 - 147
= -111
8. 11√50[tex]x^{12}y^5[/tex]
= 55[tex]x^6[/tex]y²√2y
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[tex]What is the \sqrt{555}[/tex]
Answer:
23.558
Step-by-step explanation:
u know how the thing goes
please answer immeaditaly thanks so mu ch
Answer:
2: 0.6
3: 0.1
Step-by-step explanation:
You have decided that you will choose from an integer valued x so that you do not have to cut out a fraction of an inch. What value of x should you choose? Explain why that is the best choice and why it can't be 12 inches instead? Determine the dimensions of your finished rectangular box.
Answer:
To avoid cutting out a fraction of an inch, we need to choose a value of x that is a factor of both 36 inches and 48 inches, since those are the lengths of the sides of the rectangular sheet of cardboard we are using.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The largest factor that both 36 and 48 have in common is 12. However, we can't choose x to be 12 inches because that would mean the length and width of the rectangular box would also be 12 inches, which is too small for our purposes.
Therefore, we should choose x to be the next largest factor that both 36 and 48 have in common, which is 6 inches. This means we will cut six 6-inch by 8-inch rectangles from the cardboard sheet.
The dimensions of the rectangular box will be:
Length = 2x + 2h = 2(6 in) + 2(8 in) = 12 in + 16 in = 28 in
Width = 2x + 2w = 2(6 in) + 2(12 in) = 12 in + 24 in = 36 in
Height = h = 8 in
Therefore, the dimensions of the rectangular box are 28 inches by 36 inches by 8 inches
5/6/p = 2/3/1/2 Enter answer as a simplified fraction in the box. show all work
The value of p is 5/8
What are complex fraction?A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.
Examples of complex fraction include ½/¾, ⅚/½
⅚/p = ⅔/½
= 5/6 ÷ p = ⅔ ÷ 1/2
= 5/6 × 1/p = 2/3 × 2/1
= 5/6p = 4/3
15 = 24p
divide both sides by 24
p = 15/24
p = 5/8
therefore the value of p is 5/8
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ANSWER THE FOLLOWING
For a cardboard:
Area = (d) 8400 cm²Area in sqm = (b) 0.84 m(b) 3700 cm². (b) 4700 cm².(a) ₹11.75.How to calculate area and cost of painting?The area of the cardboard is:
Length = 1 m 5 cm = 105 cm
Breadth = 80 cm
Area = Length x Breadth = 105 cm x 80 cm = 8400 cm²
The area of the cardboard in square meters is:
1 m = 100 cm
Length = 1 m 5 cm = 105 cm = 1.05 m
Breadth = 80 cm = 0.8 m
Area = Length x Breadth = 1.05 m x 0.8 m = 0.84 m²
The area covered by the ribbons is the area of the cardboard that is not painted. From the previous calculations, we know that the area of the cardboard is 8400 cm² and the area that was painted is 4700 cm². Therefore, the area covered by the ribbons is:
Area covered by ribbons = Total area of the cardboard - Area that was painted
Area covered by ribbons = 8400 cm² - 4700 cm²
Area covered by ribbons = 3700 cm²
The area of the cardboard is (105 cm) x (80 cm) = 8400 cm².
The area covered by the ribbons is 3700 cm².
So, the area of the cardboard that was painted is 8400 cm² - 3700 cm² = 4700 cm².
The area of the cardboard is 8400 cm² or 0.84 m². The area covered by the ribbons is 3700 cm². So, the area that needs to be painted is the difference between the area of the cardboard and the area covered by the ribbons, which is:
8400 cm² - 3700 cm² = 4700 cm²
To convert to square meters, we divide by 10000:
4700 cm² ÷ 10000 = 0.47 m²
Therefore, the cost of painting the remaining area is:
0.47 m² × ₹25/m² = ₹11.75
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The dimensions of a rectangular prism are (x + 1) feet by (x + 2) feet by 4 feet. The volume of the prism is (24x - 1) cubic feet. What is the value of x?
Answer:
x=3/2
Step-by-step explanation:
(x+1)(x+2)(4) = (24x-1)
4(x^2+3x+2) = 24x-1
4x^2+12x+8 = 24x-1
4x^2-12x^2+9 = 0
(2x-3)^2 = 0
2x-3 = 0
x = 3/2
The possible values of variable {x] are -
{x} = 1.146 or {x} = 1.854.
What is volume?Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write → V = ∫∫∫ F(x, y, z) dx dy dz.Given is that the dimensions of a rectangular prism are (x + 1) feet by (x + 2) feet by 4 feet.
We can write the volume of the rectangular prism as -
Volume = length x width x height
4(x + 1)(x + 2) = (24x - 1)
(x + 1)(x + 2) = 6x - 1/8
6x - (x + 1)(x + 2) = 1/8
Solving the equation graphically, we get -
x = 1.146 or x = 1.854
Therefore, the possible values of variable {x] are -
{x} = 1.146 or {x} = 1.854.
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What is 101 Inches in Feet?
Answer:
8.417
Step-by-step explanation:
The amount of 101 inches is equal to 8.4167 feet.
To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in 1 foot.
As 1 foot= 12 inches
Therefore, to convert 101 inches to feet, we divide 101 by 12:
= 101 inches / 12 inches/foot
= 8.4167 feet
So, 101 inches is equal to 8.4167 feet.
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Interval notation for x<-5
Please ASAP
Answer: (-∞, -5)
Step-by-step explanation:
When plotted on a line graph there will be an open circle on negative five and your line would be going infinitely off to the left.
The total land are of the United States is about 3,483,511 square miles more than the total land are of Tennessee, which is about 53,927 square miles. Write and solve and equation to find the total land are of the United States.
The total area of the US is equal to 3,537,438 square miles.
What is an equation?An equation is an expression shows the relationship between two or more numbers and variables.
A equation is a statement with two equal sides and an equal sign in between. An equation is, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, is about 53,927 square miles.
We need to write and solve an equation to find the total land area of the United States.
Now, according to the given information,
Total land area of the United States is 3,483,511 square miles more than the total land area of Tennessee, is 53,927 square miles
Total land area = 3,483,511 + 53,927
= 3,537,438
Hence, the total area of the US = 3,537,438 square miles.
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A sundae cost 2 dollars additional topings 0.50 write and graph the equation of two variables
Let x be the number of toppings and y be the cost of the sundae. We know that a sundae costs $2 without any toppings, and each topping costs $0.50. Therefore, the equation that describes the relationship between x and y is:
y = 2 + 0.5x
This equation can be represented on a graph, with x on the horizontal axis and y on the vertical axis. As x increases, y increases by $0.50 for each additional topping. The graph will be a line with a slope of 0.5 and y-intercept of 2, meaning that the line passes through the point (0,2) and rises by $0.50 for each unit increase in x.