Write the linear function represented by the table

12/3/2020

Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 -5
2 -8
3 -11
4 -14

Find the slope of the line by finding the change in y over the change in x, using the first two points.

(1,-5) and (2,-8) {first two points}

-8 - (-5)
---------- = slope {change in y over change in x}
2 - 1

slope = -3 {simplified}

Substitute the coordinates of one point, along with the slope, into slope-intercept form,
to find the y-intercept.

(1,-5) , m = -3 {first point and slope}
y = mx + b {slope-intercept form}
-5 = -3(1) + b {substituted}
-5 = -3 + b {multiplied}
b = -2 {added 3 to each side}

slope = -3 and y-intercept = -2

Substitute slope and y-intercept into slope-intercept form to get the equation of the linear function.

y = mx + b {slope-intercept form}
y = -3x - 2 {substituted}

f(x) = -3x - 2 {wrote in function notation}