Question

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

Answer 1

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Answer 2

One way to do this when the equation is in standard form is to note that the lines of the equations

Ax + By = C1

and

Bx - Ay = C2

are perpendicular. Therefore, a line perpendicular to 5x - 2y = -6 must take the standard form 2x + 5y = C.

Substituting x = 5, y = -4, we get

C = 2(5) + 5(-4) = 10 - 20 = -10.

Thus, 2x + 5y = -10 is correct.

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