James C. answered 12/20/17
Tutor
New to Wyzant
Experienced High School and College Math Teacher
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 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)