Answer:
y = (10/7)x - 16/7
Explanation:
The equation of a line that passes through two points (x1, y1) and (x2, y2) is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ \text{ Where} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]So, replacing (x1, y1) = (3, 2) and (x2, y2) = (-4, -8), we get:
[tex]m=\frac{-8-2}{-4-3}=\frac{-10}{-7}=\frac{10}{7}[/tex][tex]y-2=\frac{10}{7}(x-3)[/tex]Finally, we can solve the equation for y
[tex]\begin{gathered} y-2=\frac{10}{7}x-\frac{10}{7}(3) \\ \\ y-2=\frac{10}{7}x-\frac{30}{7} \\ \\ y=\frac{10}{7}x-\frac{30}{7}+2 \\ \\ y=\frac{10}{7}x-\frac{16}{7} \end{gathered}[/tex]Therefore, the answer is
y = (10/7)x - 16/7
