Question

What is the $y$-intercept for the straight line $2x-3y=5$?

Answer 1

Find the $\mathbf{y}\mathbf{-}\mathbf{intercept}$ for the straight line $\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{}\mathbf{3}\mathbf{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$:

Given equation of the straight line is rephrased as follows:

$\begin{array}{rcl}2x-3y& =& 5\\ & \Rightarrow & 3y=2x-5\\ & \Rightarrow & y=\frac{2}{3}-\frac{5}{3}\end{array}$.

Compare the obtained equation withthe general equation of line, $\mathbf{y}\mathbf{=}\mathbf{mx}\mathbf{+}\mathbf{c}$:

We get,

$\mathrm{Slope}:\mathrm{m}=\frac{2}{3}$

$\mathrm{y}-\mathrm{intercept}:\mathrm{c}=-\frac{5}{3}$.

Therefore, the $\mathbf{y}\mathbf{-}\mathbf{intercept}$ for the straight line $\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{}\mathbf{3}\mathbf{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$ is $-\frac{\mathbf{5}}{\mathbf{3}}$.