Question

what is the slope of the line?
$3x - 4y = 7$
choose 1 answer:
a $dfrac{3}{4}$
b $dfrac{3}{7}$
c $dfrac{4}{3}$
d $dfrac{7}{3}$

Explanation:

Step1: Rewrite in slope - intercept form

We want to rewrite the equation \(3x - 4y=7\) in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
First, isolate \(y\) terms: \(- 4y=-3x + 7\)

Step2: Solve for \(y\)

Divide each term by \(-4\): \(y=\frac{-3x}{-4}+\frac{7}{-4}\), which simplifies to \(y = \frac{3}{4}x-\frac{7}{4}\)
In the slope - intercept form \(y = mx + b\), the coefficient of \(x\) (\(m\)) is the slope. So the slope \(m=\frac{3}{4}\)

Answer:

A. \(\frac{3}{4}\)