Question

What is the equation of the line that passes through (-2,4) (-6,10)

Answer 1

Answer:

$\large\boxed{y-4=-\dfrac{3}{2}(x+2)}\to\boxed{y=-\dfrac{3}{2}x+1}\to\boxed{3x+2y=2}$

Step-by-step explanation:

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

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

m - slope

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

We have the points (-2, 4) and (-6, 10). Substitute:

$m=\dfrac{10-4}{-6-(-2)}=\dfrac{6}{-4}=-\dfrac{6}{4}=-\dfrac{3}{2}\\\\y-4=-\dfrac{3}{2}(x-(-2))\\\\y-4=-\dfrac{3}{2}(x+2)$