Question:
Reduce the equation 2x – 3y – 5 = 0 to slope-intercept form, and find from it the slope and y-intercept.
Solution:
Given equation is $2 x-3 y-5=0$
We can rewrite it as 2x – 5 = 3y
$\Rightarrow 3 y=2 x-5$
$\Rightarrow y=\frac{2}{3} x-\frac{5}{3}$
This equation is in the slope-intercept form i.e. it is the form of
$\mathrm{y}=\mathrm{m} \times \mathrm{X}+\mathrm{c}$, where $\mathrm{m}$ is the slope of the line and $\mathrm{c}$ is $\mathrm{y}$-intercept of the line
Therefore, $\mathrm{m}=\frac{2}{3}$ and $\mathrm{c}=-\frac{5}{3}$
Conclusion:
Slope is $\frac{2}{3}$ and $y-$ intercept is $-\frac{5}{3}$