Question

Which of the following point-slope form equations could be produced with the points (-5, -2) and (1, 2)?

Answer 1

The point-slope form:

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

We have the points (-5, -2) and (1, 2). Substitute:

$m=\dfrac{2-(-2)}{1-(-5)}=\dfrac{2+2}{1+5}=\dfrac{4}{6}=\dfrac{2}{3}\\\\y-(-2)=\dfrac{2}{3}(x-(-5))\\\\\y+2=\dfrac{2}{3}(x+5)\to c.$