Question

Write an equation to model the table in slope-intercept form.​

Answer 1

The answer is: y = 9x - 7.

Explanation:

Given the points: (3,20), (4,29), (7,56), (10,83), write an equation in the slope-intercept form.

First find the slope:

m = (y2 - y1) / (x2 - x1)

By substitution:

m = (29-20) / (4 - 3)

m = 9 / 1 = 9

Now that we have the slope, take any point and then use the slope intercept form of a line to solve for b. We will use (3,20):

y = mx + b

20 = 9*3 + b

20 - 27 = b

b = -7

By substitution:

y = 9x - 7

You can prove the equation by using another point, (7,56):

y = 9*7 - 16

y = 63 - 7 = 56

This proves that f(7) = 56, for the point (7,56)

Answer 2

y=9x-7

Explanation:

first pick any two points to plug into the equation that finds the slope

y2-y1 all over x2-x1

i picked (4,29) and (7,56)

plug in: 56-29/7-4

solve: 27/3 simplified: 9

plug it into point slope form

y-y1=m(x-x1)

now use your first point (4,29)

plug it in: y-29=9(x-4)

distribute: y-29=9x-36

add 29 to both sides: y=9x-7