Question

write an equation for the line that passes through (5,-4) and is perpendicular to the graph of 5x -2y=-6

Answer 1

Answer:

y = (-2/5)x - 2

Step-by-step explanation:

One way to attack this problem is to interchange the coefficients of x and y and change the sign of one to +:  5x - 2y = -6 becomes 2x + 5y = c.  Solving for the slope, m, we get 5y = -2x + c first, and then y = (-2/5)x + D.

Subbing 5 for x and -4 for y, we now have -4 = (-2/5)(5) + D.

Then -4 = -2 + D, so that D = -2.

The desired equation is thus y = (-2/5)x - 2.

Check:  Does this pass through (5, -4)?  Is -4 = (-2/5)(5) - 2 true?  Yes.

Is the slope -2/5 the negative reciprocal of 5/2?  Yes, it is.