Question

What is the equation in point-slope form of a line that passes through the points (−4, −1) and (5, 7) ? y+1=89(x+4) y+4=98(x+1) y−1=89(x−4) y+1=87(x+4)

Answer 1

The point-slope formula:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

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

Substitute:

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