Answer:
[tex]y=\frac{4}{3}x+\frac{10}{3}[/tex]Given:
A (5, 10)
B (-13, -14)
First, let us find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{-14-10}{-13-5}[/tex][tex]m=\frac{-24}{-18}[/tex][tex]m=\frac{4}{3}[/tex]Next, we will use the following formula to solve for the equation of the line
[tex]y=mx+b[/tex]Using the point A (5, 10), and the slope, solve for b
[tex]10=(\frac{4}{3})(5)+b[/tex][tex]10=\frac{20}{3}+b[/tex][tex]10-\frac{20}{3}=b[/tex][tex]\frac{10}{3}=b[/tex]Now that we have the slope m, and the value of b, substitute it to this equation to get the equation of the line
[tex]y=mx+b[/tex][tex]y=\frac{4}{3}x+\frac{10}{3}[/tex]