Question

Which choice is the equation of a line that passes through the point (–2, 8) and is perpendicular to the line represented by this equation? 5x − 2y = −10

A. 2x− 5y = 26
B. 5x + 2y = 10
C. 2x + 5y = 36
D. −2x + 5y = −13

Answer 1

Answer:

C. 2x + 5y = 36

Step-by-step explanation:

$\text{If}\ A_1x+B_1y=C_1\ \text{is perpendicular to}\ A_2x+B_2y=C_2,\ \text{then}\\\\\dfrac{A_1}{B_1}=-\dfrac{B_2}{A_2}.\\\\\text{We have the equation:}\ 5x-2y=-10\to A_1=5,\ B_1=-2.\\\\\dfrac{A_1}{B_1}=\dfrac{5}{-2}\to-\dfrac{B_2}{A_2}=-\dfrac{5}{2}\qquad\text{change the signs}\\\\\dfrac{B_2}{A_2}=\dfrac{5}{2}\to A_2=2,\ B_2=5\\\\\text{Therefore the equation of a perpendicular line is:}\\\\2x+5y=C\\\\\text{Put the coordinates of the given point and solve for}\ C:\\\\2(-2)+5(8)=C\\\\C=-4+40\\\\C=36\\\\\text{Finally:}\\\\2x+5y=36$