1. Find the equation of the line that goes through the points (2, 5) and (4, 7).

We use the formula for the slope.

If

(x1, y1) = (2, 5)

and

(x2, y2) = (4, 7)

Then

= 1

Next use the point slope form of the equation.

y - y1 = m(x - x1)

y - 5 = 1(x - 2)

Simplify

y - 5 = x - 2

Transpose

y = x - 2 + 5

y = x + 3

Note that in each point, the y coordinate is 3 more than the x coordinate.