First, lets find the slope intercept form (mx + b = y) of the first line. Slope is found by the equation [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex].
[tex] \frac{4 - (-6)}{-2 - 0} [/tex]
[tex] \frac{10}{-2} = -5 [/tex]
So the slope of the first line is -5. We already know the y-intercept, so we don't need to solve for it. The first equation is -5x -6 = y.
For a line to be perpendicular, its slope must be the opposite reciprocal of the given line. In this case, the perpendicular line would have the slope of 1/5.
We then input the point given into the equation 1/5x + b = y to find b.
1/5(5) + b = -4
1 + b = -4
b = -5
Therefore the equation of the perpendicular line is 1/5x - 5 = y
