"Find an equation for the family of linear functions with slope 4. (Use the standard coordinate variables x and y. You may use m for the slope and b for the y-intercept as needed.)"

An equation for the family of linear functions with slope 4 is; y = 4x +b

The equation of a line can be determined by means of the slope as follows;

Therefore, for this scenario;

By Cross-product, we have;

Since, the y-intercept, b is the value of y for which x= 0.

Hence;

Read more on slope-intercept form;

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Y= 4x +y1-4x1

4 represent the slope m

+Y1 - 4x1 represent the intercept b

Step-by-step explanation:

Formula for the equation of the linear function

(Y-y1)/(x-x1) = m

We will transform it into the equation form

Y= mx + b

Where m = slope=4

b = intercept

(Y-y1)/(x-x1) = m

(Y-y1)/(x-x1) = 4

(Y-y1)= 4(x-x1)

Y-y1= 4x -4x1

Y= 4x +y1-4x1

4 represent the slope m

+Y1 - 4x1 represent the intercept b