Write an equation perpendicular to 5x + 3y = -21 that passes through the point (-5, 1).

the desired equation is y = (3/5)x + 4

Step-by-step explanation:

Solving the given 5x + 3y = -21 for 3y yields  3y = -5x - 21.  Dividing all three terms by 3, we get:

y = (-5/3)x - 7, indicating that the given line has slope -5/3.

The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.

Start with y = mx + b.  Substitute 1 for y, -5 for x and 3/5 for m.  Then:

1 = (3/5)(-5) + b, or

1 = -3 + b.  Then b must be 4, and so the desired equation is y = (3/5)x + 4.