Question

Write an equation for the line in point slope form through the points (2, −6) and (−1, −8).

Answer 1

Let point A be $(2, -6)$ and point B $(-1, -8)$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - (-6)}{-1 - 2} = \frac{-8 + 6}{-1 -2} = \frac{-2}{-3} = \frac{2}{3}$

Use the point-slope formula and whichever point you want as , in this case I'll use

$y - y_1 = m(x - x_1)\\y - (-6) = \frac{2}{3}(x - 2)\\y + 6 = \frac{2}{3}x - \frac{4}{3}\\y = \frac{2}{3}x - \frac{4}{3} - 6\\y = \frac{2}{3}x - \frac{14}{3}$