Question

What is the equation in point-slope form of a line that passes through the points (−4, −1) and (5, 7) ?

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)$

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-4, -1) and (5, 7). Substitute:

$m=\dfrac{7-(-1)}{5-(-4)}=\dfrac{7+1}{5+4}=\dfrac{8}{9}\\\\\boxed{y-7=\dfrac{8}{9}(x-5)}$