Write the standard form of the equation of the line through (3, -2) and perpendicular to y = 5x +4.

x + 5y = -7

Step-by-step 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)