Construct a linear function that has a slope of -3 and passes through the point (−2,3)

Answer:

f(x) = -3x - 3

Step-by-step explanation:

you can use the point-slope form to help you.  

[tex]y - y_{1} = m (x - x_{1} )[/tex]     m = slope   and  [tex](x_{1} , y_{1}) = (-2, 3)[/tex]

So,  y - 3 = -3(x + 2)

y - 3 = -3x - 6

y = -3x - 3    or f(x) = -3x - 3

[tex]f(x) = -3x - 3[/tex]You can use the standard form y = mx + c to build that linear relationship.

Thus, the needed linear function is: [tex]f(x) = -3x -3[/tex]

The linear function

A linear function of two variables is always an equation of a straight line and can be converted into standard form y = mx + c (assuming m and c to be finite constants and x and y are variables).

m denotes slope of this line and c denotes intercept on y axis by this line.

If linear function is not of two variables, then we can take the output f(x) as value of second variable.

Since the slope is already given, thus, we have the equation as:

y = -3x + c

Now, since the line passes through (-2,3), thus it must satisfy the equation since the point is member of the family of points who constitute this line(and since the equation shows family of such points, thus the point should satisfy the equation).

Thus,

[tex]y = -3x +c|{(x,y) = (-2,3)}\\ 3 = -3 \times -2 + c\\ 3 = 6 + c\\ c = 3 - 6\\ c = -3[/tex]

Thus, we have the equation of the straight line in consideration as:

y = -3x -3

y is function of x, thus can be rewritten as  [tex]f(x) = -3x -3[/tex] (assuming f doesn't represent any other function as we can't use used symbols in a context to prevent ambiguity)

Thus, the needed linear function is: [tex]f(x) = -3x -3[/tex]

Learn more about equation of straight line here:

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