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. y = –x – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –(x – 5) y – 4 = (x + 5)

Answer 1

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 a correct choice.

 This can be rewritten in slope-intercept form:

 2x + 5y = -10

2x + 5y - 2x = -10 - 2x

5y = -2x - 10

5y / 5 = (-2x - 10) /5  

y = -(2/5) x - 2

 Note that the slope is -2/5 and it passes through (5, -4) Therefore, its point-slope form is  

 y - y1 = m(x - x1)

y + 4 = -(2/5)(x - 5)