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

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.