Question

Which of the following are point-slope equations of the line going through (-5,6) and (1,1)?

Answer 1

Answer:

$A.\ y-6=-\dfrac{5}{6}(x+5)\\\\B.\ y-1=-\dfrac{5}{6}(x-1)$

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

The formula of a slope:

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

We have the points (-5, 6) and (1, 1). Substitute:

$m=\dfrac{1-6}{1-(-5)}=\dfrac{-5}{6}\\\\\text{For point (-5, 6):}\\\\y-6=-\dfrac{5}{6}(x-(-5))\\\\y-6=-\dfrac{5}{6}(x+5)$

$\text{For point (1, 1):}\\\\y-1=-\dfrac{5}{6}(x-1)$