Question

what is an equation of the line that passes through the points $(6, 5)$ and $(7, 7)$?

Explanation:

Step1: Calculate slope $m$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{7 - 6} = 2$

Step2: Use point-slope form

$y - y_1 = m(x - x_1)$
Substitute $m=2$, $(x_1,y_1)=(6,5)$:
$y - 5 = 2(x - 6)$

Step3: Simplify to slope-intercept form

$y - 5 = 2x - 12$
$y = 2x - 7$

Answer:

$y = 2x - 7$