Question

Find the slope and y-intercept of the lines $3x-4y=5$.

Answer 1

We solve the given line $3x-4y=5$ for $y$ as follows:

$3x-4y=5\Rightarrow 4y=3x-5\Rightarrow y=\frac{3x-5}{4}\Rightarrow y=\frac{3}{4}x+(-\frac{5}{4})......\left(1\right)$

We know that the equation of a line is $y=mx+c$ where $m$ is the slope of the line and $c$ is the y-intercept.

Comparing the equation of line $y=mx+c$ with equation 1 we have,

$m=\frac{3}{4}$ and $c=-\frac{5}{4}$

Hence, the slope of the line is $\frac{3}{4}$ and the y-intercept is $-\frac{5}{4}$.