Question

What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1)?
y + 1 = 6/7 (x+4)
y + 4 = 11/6 (x+1)
y − 1 = 6/11 (x−4)
y + 1 = 6/11 (x+4)

Answer 1

The point-slope form:

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

m - slope

(x₁, y₁) - point

The formula of a slope:

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

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

$m=\dfrac{-1-5}{-4-7}=\dfrac{-6}{-11}=\dfrac{6}{11}$

$y-(-1)=\dfrac{6}{11}(x-(-4))\\\\\boxed{y+1=\dfrac{6}{11}(x+4)}$