Question

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

x y
-4 0
1 5
6 10
11 15

Answer 1

the desired equation is y = x + 4.

Explanation:

Slope is defined as m = rise over run. Run is the change (usually an increase) in x, and rise an increase or decrease in y.

We see, in the table, that if x increases from 1 to 6 (a 'run' of 5), y increases from 5 to 10 (a 'rise' of 5). Thus, it's immediately apparent that the slope is m = rise / run = 5 / 5, or just 1.

Using the slope-intercept form of the equation of a straight line, y = mx + b, and the point (1, 5), we calculate b:

5 = 1(1) + b, or b = 4.

Therefore the desired equation is y = x + 4.