Answer:
The equation of the line would be y = -2/5x - 2
Step-by-step explanation:
In order to find this, we first need to find the slope of the first equation. We can do this by solving for y.
5x - 2y = -6
-2y = -5x - 6
y = 5/2x + 3
Now that we have the slope of 5/2, we know that the perpendicular slope is -2/5. We know this because it is the opposite and reciprocal. Now, we can use this along with a point to solve in point-slope form.
y - y1 = m(x - x1)
y - -4 = -2/5(x - 5)
y + 4 = -2/5x + 2
y = -2/5x - 2
