Question

Time (h), z
Distance from Home (mi), y
2
12
5
18
8
24
>>First, substitute the rate of change into the equation.
y = mx + b
y=
X
7
8
9X
4 5 6
1
2
3
0
(-)
rate of change: 2

Answer 1

First find the slope m:
m = (18 − 12) / (5 − 2) = 6 / 3 = 2.

Substitute m into y = mx + b:
y = 2x + b.

Use a point to find b (use x=2, y=12):
12 = 2(2) + b → 12 = 4 + b → b = 8.

So the linear equation is
y = 2x + 8.

(Check: for x=5, y = 2·5+8 = 18; for x=8, y = 24.)