Write a rule for the linear function shown in the graph.
y = 4x – 3
y = –x + 4
y = 2x + 5
y = 1/4x +1
Answers
Answer: Answer is A. y = 4x - 3
Graph the line using the slope and y-intercept, or two points.
Slope: 2/ 5
y-intercept: ( 0 , − 1 )
x y
0 − 1
5/ 2 0
Step-by-step explanation:
How do you graph y=4x-3?
In graphing an equation, a very valuable graphing technique is the ability to recognize the kind of graph that a certain type of equation produces.
Any equation that is of the form y = mx + b is in the "slope-intercept" form for the equation of a straight line, where x and y are variables, where “m” is a real number representing the slope of a line, and where “b” is a real number representing the y-intercept of a line , i.e., the y-coordinate of the point of intersection between a straight-line graph and the y-axis.
Since the given equation y = 4x ‒ 3 is in the slope-intercept form, where m = 4 and b = ‒3, then it’s a linear equation and its graph is a straight line. Also, looking at the given equation, we know that the independent variable x can take on any real number as a replacement.
Now that we know that the graph of the given equation is a straight line and that there are no restrictions on the variable x, we need to determine and then draw the straight-line graph on a Cartesian (rectangular) coordinate system with the y-axis as the vertical axis and the x-axis as the horizontal axis. We know that two points determine a straight line; So, all we need to do is find the point where the straight-line graph of the given equation y = 4x ‒ 3 intersects the x-axis, i.e., the point of the x-intercept, and find the point where the straight-line graph of y = 4x ‒3 intersects the y-axis, i.e., the point of the y-intercept. Also, it would be a good idea to plot a third point as a check.
(1.) Determining the point of the x-intercept:
For any point on the x-axis, the y-coordinate is zero; therefore, in our given equation, let y = 0 and solve for x as follows:
y = 4x ‒3
0 = 4x ‒3
0 + 3 = 4x ‒3 + 3
(1/4)(4x) = (1/4)(3)
x = 3/4
Therefore, the x-intercept is x = 3/4, and the graph of the given equation y = 4x ‒3 intersects the x-axis at the point (3/4, 0).
(2.) Determining the point of the y-intercept:
To get the y-intercept, we can simply select it from the given equation y = 4x ‒3 which is already in slope-intercept form (y = mx + b), i.e., y = 4x ‒3 or y = 4x + (‒3); therefore, the y-intercept of the straight-line graph of the given equation is y = b = ‒3, which is the y-coordinate of the point of intersection between the straight-line graph of the given equation and the y-axis. Also, for any point on the y-axis, the x-coordinate is zero; therefore, the straight-line graph of the given equation intersects the y-axis at the point (0, ‒3).
(3.) Check Point
In generating a third point as a check point, choose a convenient value for x so that the corresponding value for the dependent variable y is nice and even. Let x = 2, then:
y = 4x ‒3
= 4(2)‒ 3
= 8 ‒ 3
y = 5
Consequently, the third point (check point) on the straight-line graph of the given equation is (2, 5).
(4.) Plot the points
Now, create the straight-line graph of the given equation by plotting the three points: (3/4, 0), (0, ‒3), and (2, 5) on a Cartesian (rectangular) coordinate system, and then use a straight edge to draw the straight line through all three plotted points. Draw the line past the two outer points and then draw an arrowhead at each “end” of the line to show that the line goes on indefinitely in both directions. NOTE: If the third point (2, 5)(the check point) is not on the drawn line, then go back and look for an error. The error was either made in finding the x- and y-intercepts, or the error was made in generating the coordinates of the check point, or both. When the error is found, make the appropriate correction(s), and then redraw the graph (straight line) of the given equation.
These are four steps that you can use to graph the given equation y = 4x ‒3 or any equation that is in the slope-intercept form for the equation of a straight line: y = mx + b.
Related Questions
A triangular prism where the base is a right traingle with lengths of the edge are given 3cm,4cm,5cm,3cm what are the total surface
Answers
Answer:
Total surface area is 48 square Centimeter
Step-by-step explanation:
Total surface area is equal to the product of triangular base area and the height of the prism
Area calculation of triangular base
[tex]S = \frac{3+4+5}{2} = 6\\[/tex]
Area =
[tex]\sqrt{S(S-a)(S-b)(S-c)}[/tex]
Substituting the given values in above equation we get
[tex]\sqrt{6 *3*2*1} = 6[/tex] square centimeter
Total surface area
= [tex]2 * 6 + (3*3)+(3*4)+(3*5)\\= 12 + 9 + 12+ 15\\= 48[/tex] square Centimeter
What is the tax on a $7.40 item if the sales-tax rate is 8%?
Answers
Answer:
$7.99
Step-by-step explanation:
7.4*0.08 = 0.592 (0.59)
7.4 + 0.59 = 7.99
Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday. On Tuesday, she has 7/9 the number of pens she had on Monday. On Wednesday, she has 2/7 of the number of pens she had on Tuesday.
How many packages of pens does she have on Wednesday?
Answers
Answer:
No but she can have dezzz nuts
Step-by-step explanation:
solve for x: 3(x + 1) = −2(x − 1) + 6.
Answers
Answer:
x=1
Step-by-step explanation:
3(x+1)=-2(x-1)+6
3x+3=-2x+2+6
3x+2x=2+6-3
5x=8-3
5x=5
x=[tex]\frac{5}{5}[/tex]
x=1
A car travels 45 miles on one gallon of gas.The car uses 10 gallons of gas.How many miles does it travel
Answers
Answer:
69
Step-by-step explanation:
A car travels 45 miles on one gallon of gas.The car uses 10 gallons of gas.How many miles does it travel
Answer:
it travels 450 miles on 10 gallons of gas.
Step-by-step explanation: Can I get the brainliest answer if it's correct.
y = 2x - 15 y = 5x solve using systems of equations
Answers
Answer:
The answer will be (-5,-25) or x= -5 and y=-25
Step-by-step explanation:
Hope this helped
Answer:
Step-by-step explanation:
Since the solution will occur when y=y
2x-15=5x
-3x-15=0
-3x=15
x=-5, using this in y=5x
y=5(-5)
y=-25 so the solution is the point
(-5, -25)
I need help on this question as soon as possible
Answers
Answer:
choice 2) rotation 90 CW
Step-by-step explanation:
Answer:
Rotation 90 CW
Step-by-step explanation:
Can I have Brainliest?
The team ratio of games won to games played was 2 to 7. If the team played 49 games, how many games did the team fail to win?
Answers
Answer:
they failed to win 35 games
Someone plz help me
I will give brainliest!!
Answers
Answer:
3) fifty seven and three tenths
4) 1, 2, 4, 8, 16
5) No, she would have only 60 pictures in the album. When she has 80 pictures in total. 15×4=60
Step-by-step explanation:
Hope this Helps!!
:)
write an equation that has the solution of X equals Y
Answers
Answer:
Step-by-step explanation:
The system of equations x + y = 1 and x – y = 2 has the unique solution x = 1 and y = –1.
There are infinite pairs of system of equations which have the unique solution x = 1 and y = –1.
Hope this information will clear your doubts about the topic.
How can I solve this question?
Answers
draw a rectangle triangle :
sin B=8/17 that means that de biggest side are 17 ("hipotenusa"), and another side is 8. Applying de theorem of pythagoras:
[tex]17^{2} =8^{2} +x^{2} \\x^{2} =17^{2} -8^{2}\\x=\sqrt{17^{2} -8^{2}} \\x=5\sqrt{5}[/tex]
Today only, a sofa is being sold at a 35% discount. The sale price is $559.
What was the price yesterday?
Answers
Answer:
195.65
Step-by-step explanation:
Answer:
100%-29% = 71%
568/0.71 = 800
price was $800
Step-by-step explanation:
If I'm wrong I'm sorry
If I'm right Thank you and (Brainliest plz )
35 points!!! Help!! Make sure u answer all!!!
Answers
Answer:
Expression for Perimeter: 6x + 6
x = 12 cm
Verify A = 360:
2(12) x (12+3) = 360
24 x 15 = 360
360 = 360
Step-by-step explanation:
I need some help with this question
Answers
9514 1404 393
Answer:
terms: 2
degree: 1
Step-by-step explanation:
The expression has two terms, separated by a minus sign.
The degree of the expression is the exponent of the only variable, 1. (Typically, a coefficient of 1 and/or an exponent of 1 are not shown.)
terms: 2; degree: 1
Help this is timed!!!
Answers
Answer:
C. (4,2)
Step-by-step explanation:
The point where the lines intersect is (4, 2)
Answer:
IT IS 2,4!!!!!!!!!1
Step-by-step explanation:
Jason wants to create a box with the same volume as the one shown below. He wants the length to be 4inches. What would be the measurements of the width and height?
Answers
whats the anwser for 14−3x<−1
Answers
Answer:
Step-by-step explanation:
Here you go mate
Step 1
14−3x<−1 Question
Step 2
14−3x<−1 Simplify
Step 3
14−3x<−1 Subtract 14 from sides
-3x<-15
Step 4
-3x<-15 Divide sides by -3
x>5
Answer
x>5
Hope this helped
Answer:
Step-by-step explanation:
I can help
Step 1
14−3x<−1 Simplify
Step 2
14−3x<−1 subtract 14 from the sides
-3x<-15
Step 3
-3x<-15 Divide the sides by 3
-3x/-3<-15/-3
Answer
x>5
Hope this helps
*
Simplify the square root
V16
O
16
0.4
O
40
O
4
Answers
4
Step by step:
The square root of 16 is 4. To check, multiply 4 on itself (4x4) to see if the answer is 16.
because 4² = 4×4 = 16
answer is option A
Find the distance between
Answers
Answer:
4,3
Step-by-step explanation:
Edunuity sucks;-;
hi-
Jada’s sister works in the furniture store. The store bought a table for $200, and sold it for $350. What percent was the mark up?
Answers
Answer:
75%
Step-by-step explanation:
350-200=150
150 is 75% of 200
Answer:
175%
Step-by-step explanation:
350/200 = 175/100
Sorry if it doesn't make sense but if it was 75% then it would be lower than original price.
Gilbert took 2 hours longer to drive 240 miles on the first day of a business trip than to drive 144 miles on the second day. If his rate was the same both days, what was his driving time for each day?
Answers
Answer:
dyvhbCNN mfg beneficialgVCR specializations acknowledgement
Patty, Helene, and Mira share $0.96 that they found in an old wallet. How much money does each girl get?
Answers
Answer:
33 cents
Step-by-step explanation:
.96 divided by 3 = .36
What does (x-6) ( x-2) represent
Answers
x^2-8x+12
Step-by-step explanation:
you foil them
Two rectangular rugs are ordered at Cardi’s furniture: small rugs and large rugs.
Small rugs are 36 inches long and 18 inches wide.
Large rugs are 90 inches long and 45 inches wide.
a. Are the rugs similar shapes? Explain your reasoning.
b. Find the ratio of the two perimeters and the ratio of the two areas. Is there anything you notice about these ratios? What can you deduce?
c. It takes 180 feet of yarn to create a square foot of either rug. How many inches of yarn are needed to make the small rug? How many feet or yarn is needed to make the large rug?
d. If a “skein” of yarn costs $4.50 and one skein is exactly 180 feet of yarn, how many skeins of yarn are needed to make the large rug? Given this answer what is the lowest Cardi’s must sell the large rug in order to make a profit
PLEASE HELP EVEN IF U CAN ANSWER JUST 1
Answers
Answer:
a.) yes they are similar shapes, the width for both rugs is 1/2 of the length. This means that they are both similar in shape.
b.) 2:5 (perimeter rug 1 and 2 compared), 4:25 ( area for 1 and 2). The numers in the perimeter ratio are the square root of the numbers in the area ratio.
c.) You will need 648 sq in for the small rug and 4050 sq in for the large rug.
d.) 2: she has to sell the large rugs x>$9 and the small rugs for s>$1.50
Step-by-step explanation:
total perimeter for rug 1 = 108 For rug 2 = 270
area for run 1 = 648 For rug 2 = 4050
180 ft = 2150 in
The large rug needs two skeins of yarn which cost 9 dollars, if she wants to make a profit she will have to sell them over that price.
You can make 3 small rugs with one skein meaning if she wants to make a profit from the small rugs she has to sell them over 1/3 of the price of the skein (which is sold for $4.50). She will have to sell the small rug for over $1.50
If f(x)=3x-2 and g(x)=2x+1 find (f-g)(x)
Answers
9514 1404 393
Answer:
(f-g)(x) = x -3
Step-by-step explanation:
(f-g)(x) = f(x) -g(x)
= (3x -2) -(2x +1)
= 3x -2 -2x -1 = (3x -2x) +(-2 -1)
(f-g)(x) = x -3
Find the product. (6y − 2)2
Answers
Answer:
36y² - 24y + 4
Step-by-step explanation:
(6y - 2)² = (6y - 2)(6y - 2)
Each term in the second factor is multiplied by each term in the first factor, that is
6y(6y - 2) - 2(6y - 2) ← distribute both parenthesis
= 36y² - 12y - 12y + 4 ← collect like terms
= 36y² - 24y + 4
Given the following formula, solve for I.
P = 2(1 + b)
A
P - 0
4
OB. 1 = 4(P + b)
= P =
P - 26
OD. I =P
P – 5
OC. 1 =
2
Answers
answer: c. l =p-2b/2
step by step:
p=2(1-b)
p=2l-2b
p+2b/2=2l/2
l =p-2b/2
HELP ASAP I will mark brainliest Emmy is flying a drone in a field near her house. She placed the drone on the ground and used the controls to make it rise at a constant rate. Then, she kept the drone at the same altitude for a few minutes before bringing it back down to the ground at a constant rate. Which graph shows the drone's altitude over time ?
Answers
Answer:
It is the one on the bottom right
Step-by-step explanation:
First of all, we have to start at (0,0), so we can cross out the one on the top left and top right, as they does not.
Also, the one on the bottom right does not go back to the ground, though just stays in the air, but the one on the bottom right dows go back to the ground.
So, its the one on the bottom right
Use the graph to answer the following question.
For which interval is the function increasing and changing by a constant
rate of change?
A. between 2 and 4
B. -2 and 0
C. between -4 and -2
D. between 0 and 2
Answers
We can conclude that in the interval -4 and 2, the function increasing and changing by a constant rate of change.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is the graph of a function as shown in the image.
Between the interval -4 and 2, the function increasing and changing by a constant rate of change.
Therefore, we can conclude that in the interval -4 and 2, the function increasing and changing by a constant rate of change.
To solve more questions on functions, visit the link-
https://brainly.com/question/29014197
#SPJ5
Which expression is equivalent to 3 (x – 9) + 6?
A. 3x - 3
B. 3x - 21
C. 15 - 3x
D. 33 - 3x