Question

Which is an equation of a line perpendicular to the graph of 3x-4y=9?

Answer 1

Answer:

B. 8x + 6y = 7

Step-by-step explanation:

Lines that are parallel to each other have slopes that are opposite reciprocals of each other. Thus, find the slope of the given equation, then determine which one of the options has a slope that is the opposite reciprocal of it.

1) To find the slope of the given equation easily, put the equation in slope-intercept form, represented by the formula $y = mx + b$. Isolate y. The coefficient of the x-term, or $m$, represents the slope, thus whatever number is in place of $m$ or is the coefficient of the x-term must be the slope.

$3x-4y = 9\\-4y = -3x+9\\y = \frac{3}{4} x-\frac{9}{4}$

The slope is $\frac{3}{4}$. The opposite reciprocal of that is $-\frac{4}{3}$, so find the equation that has that slope.

2) Let's try option B, or 8x + 6y = 7. Do the same and isolate y, putting it in slope-intercept $y = mx + b$form:

$8x + 6y = 7\\6y = -8x + 7\\y = -\frac{4}{3} x+7$

This line does have a slope of $-\frac{4}{3}$, thus it is perpendicular to the original line.