Answer:
x + 5y = -7
Explanation:
A line perpendicular to y = 5x + 4 has a slope which is the negative reciprocal of 5, that is, -1/5.
The equation of this new line has the form y = mx + b, or -2 = (-1/5)(3) + b. Solving this for the y-intercept, b, we get:
-2 = -3/5 + b, which yields b = -2 + 3/5, or b = -7/5. Then the equation of the new (perpendicular) line is y = (-1/5)x - 7/5. We must convert this into standard form Ax + By = C:
Multiplying all three terms of y = (-1/5)x - 7/5 by 5 yields 5y = - x - 7, which, when rearranged, comes out to x + 5y = -7 (desired equation in standard form)