Answer :
Step 1: Write out the equation of a straight line given two points
[tex]\begin{gathered} A(x_1,y_1) \\ B(x_2,y_2) \\ \text{the equation of line AB} \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Step 2: write out the coordinates given in the question
[tex]\begin{gathered} A(-8,-2) \\ B(-4,6)_{} \\ x_1=-8;y_1=-2 \\ x_2=-4;y_2=6 \end{gathered}[/tex]Step 3: Substitute the given parameters in the formula
[tex]\begin{gathered} \frac{y--2}{x--8}=\frac{6--2}{-4--8} \\ \frac{y+4}{x+8}=\frac{6+2}{-4+8} \\ \frac{y+4}{x+8}=\frac{8}{4} \\ \frac{y+4}{x+8}=2 \end{gathered}[/tex][tex]\begin{gathered} \text{crossmultiply} \\ y+4=2(x+8) \\ y+4=2x+16 \\ y=2x+16-4 \\ y=2x+12 \end{gathered}[/tex]Hence, the equation of the line is y=2x+12