A line perpendicular to the given line should have a slope which is a negative reciprocal of the given slope.
In the given, the slope is -2/3. Thus, the new slope should be m=3/2.
To obtain the line with the slope 3/2 and passes through (4,-8), substitute the value of the slope and the coordinates into the point-slope formula and then simplify the right side of the equation.
[tex]\begin{gathered} y=m(x-x_1)+y_1 \\ y=\frac{3}{2}(x-4)+(-8) \\ y=\frac{3}{2}(x-4)-8 \\ y=\frac{3}{2}x-6-8 \\ y=\frac{3}{2}x-14 \end{gathered}[/tex]
Thus, the values for the blanks should be 3, 2, and -14, respectively.
