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

Mathematics

1 answer:

Vadim26 [7]2 years ago

6 0

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.

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