Question

Find the slope and y-intercept of the lines $2x+3y=4$.

Answer 1

We solve the given line $2x+3y=4$ for $y$ as follows:

$2x+3y=4\Rightarrow 3y=-2x+4\Rightarrow y=\frac{-2x+4}{3}\Rightarrow y=-\frac{2x}{3}+\frac{4}{3}......\left(1\right)$

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,

$m=-\frac{2}{3}$ and $c=\frac{4}{3}$

Hence, the slope of the line is $-\frac{2}{3}$ and the y-intercept is $\frac{4}{3}$.