Given: the points (-3,r) and (13,6) lie on the same line
The slope of the line = 3/4
So, we will find the value of r using the slope form as follows:
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{3}{4}=\frac{6-r}{13-(-3)} \end{gathered}[/tex]Solve the last equation for r:
[tex]\begin{gathered} \frac{3}{4}=\frac{6-r}{16} \\ \\ 3\cdot16=4(6-r) \\ 48=24-4r \\ 4r=24-48 \\ 4r=-24 \\ r=-\frac{24}{4}=-6 \end{gathered}[/tex]So, the answer will be r = -6
