Answer :
First line: (2,3) and (1,5).
We have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=2 \\ x_2=1 \\ y_1=3 \\ y_2=5 \end{gathered}[/tex][tex]m=\frac{5-3}{1-2}=\frac{2}{-1}=-2[/tex]Then, we use the point-slope formula to find the equation of the first line
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-2(x-2) \\ y=-2x+4+3 \\ y=-2x+7 \end{gathered}[/tex]The first equation is y = -2x + 7.
Second line: (5, -2) and (-16, 4).
We repeat the process we used above to find the second line.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=5 \\ x_2=-16 \\ y_1=-2 \\ y_2=4 \end{gathered}[/tex][tex]m=\frac{4-(-2)}{-16-5}=\frac{4+2}{-21}=-\frac{6}{21}=-\frac{2}{7}[/tex]Then,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-\frac{2}{7}(x-5) \\ y+2=-\frac{2}{7}x+\frac{10}{7} \\ y=-\frac{2}{7}x+\frac{10}{7}-2 \\ y=-\frac{2}{7}x+\frac{10-14}{7} \\ y=-\frac{2}{7}x+\frac{-4}{7} \\ y=-\frac{2}{7}x-\frac{4}{7} \end{gathered}[/tex]The second equation is y = -2/7x - 4/7.
