the line is perpendicular to the line:
[tex]y=-\frac{3}{4}x-2[/tex]this means that the slope of the line will be the negative reciproc of the other line so it would be:
[tex]m=\frac{4}{3}[/tex]now with the slope and the coordinate (3,8) we can find the intersection with the y axis by replacing x = 0 so
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-8=\frac{4}{3}(0-3) \end{gathered}[/tex]and we solve for y
[tex]\begin{gathered} y=-4+8 \\ y=4 \end{gathered}[/tex]So finally we can write the general equation like:
[tex]y=\frac{4}{3}x+4[/tex]where m = 4/3 and c = 4
