Question

Find the equation of the linear function represented by the table below in slope-intercept form.

Answer 1

y=-3x+4

Explanation:

The slope-intercept form of the equation of a line is y=mx+b, where m is the slope and b is the y-intercept. To find the slope, use

`m=(y_2-y_1)/(x_2-x_1)`

For this problem, let

`(x_1,y_1)=(1,1)\\(x_2,y_2)=(4,-8)`

So,

`m=((-8)-(1))/((4)-(1))\\m=(-8-1)/(4-1)\\m=(-9)/(3)\\m=-3`

Let -3 equal m in the point-slope form
`y-y_1=m(x-x_1)`, and substitute any of the ordered pairs from the table. Let

`(x_1,y_1)=(1,1)`

So,

`y-(1)=(-3)(x-1)\\y-1=-3(x-1)`

Finally, manipulate the point-slope form of the equation of a line to derive the slope-intercept form:

`y-1=-3(x-1)\\y-1=-3x+3\\(y-1)+1=(-3x+3)+1\\y=-3x+4`