Question

Need an explantion for why the correct answer is the correct answer please.

4. Which line is perpendicular to 5x+4y=8
A. 5y=4x+15
B. 4y=-5x+3
C. 5y= -4x=15
D. 4y= 5x+12
My answer: B.
Correct answer: The correct answer is A.

Answer 1

one approach

put the original equation in the form y = mx + b
the slope is m
for perpendicular lines the product of the slopes is -1. one slope m the other -1/m
now you have the slope for the perpendicular line

go through the options and see which one has the same slope as the one you calculated for the slope of the perpendicular line

Answer 2

do you know how to change
5x+4y=8
to slope-intercept form y = mx + b ?
add -5x to both sides
5x+-5x + 4y = -5x+8
the 5x+ -5x on the left add up to zero , and 0+4y is 4y
4y= -5x+8
now divide both sides (and all terms) by 4
\[ \frac{4y}{4}= \frac{-5 x}{4} + \frac{8}{4}
\]
simplify to get
\[ y= -\frac{5}{4} x + 2\]

the slope of this line is -5/4
a parallel line will have the same slope
For example, choice B
B. 4y=-5x+3
divide both sides by 4 to get
y = (-5/4) x + 3/4
choice B also has a slope of -5/4. It is a parallel line.