Question

Which is an equation of the line that passes through the points (–6, 3) and (2, 7)?

Answer 1

Step-by-step explanation:

the typical line equation is

y = ax + b

a is the slope. it is the ratio of "y coordinate change / x coordinate change".

b is the y-intercept (the y value when x = 0) indicating the point, where the line crosses the y-axis.

going from one to the other point

x changes by +8 (from -6 to 2).

y changes by +4 (from 3 to 7).

so, the slope a is +4/+8 = 1/2.

the semi-finished equation is

y = 1/2 x + b

for b we use one of the points in the equation and since for b. let's go for (2, 7) :

7 = 1/2 × 2 + b = 1 + b

6 = b

so, the full equation is

y = 1/2 x + 6