a line passes through the points (-3, -4) and (6, -10). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The formula for slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}). Here, (x_1=-3,y_1 = - 4,x_2=6,y_2=-10). (m=\frac{-10-(-4)}{6-(-3)}=\frac{-10 + 4}{6 + 3}=\frac{-6}{9}=-\frac{2}{3})

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)). Let's use the point ((x_1,y_1)=(-3,-4)) and (m =-\frac{2}{3}). (y-(-4)=-\frac{2}{3}(x-(-3))) (y + 4=-\frac{2}{3}(x + 3))

Step3: Convert to slope - intercept form

Expand the right - hand side: (y+4=-\frac{2}{3}x-2) Subtract 4 from both sides: (y=-\frac{2}{3}x-2 - 4) (y=-\frac{2}{3}x-6)

Answer:

(y =-\frac{2}{3}x-6)