Question

For the line $2x+3y=6$, the $x-$intercept is _____ and the $y-$intercept is _______.

Short answer

The intercept is given below:

$x-$intercept: $\left(3,\hspace{0.17em}0\right)$

$y-$intercept:$\left(0,\hspace{0.17em}2\right)$

Step-by-step solution

Step 1. Given information.

We have:

$2x+3y=6$

Step 2. Find intercepts.

$x-$intercept: It is point where $y=0$.

role="math" localid="1645792645850" $$\begin{gathered} 2x+3\left(0\right)=6 \\ 2x=6 \\ x=\frac{6}{2} \\ x=3 \end{gathered}$$

$\mathrm{X}\hspace{0.17em}\mathrm{Intercepts}:\hspace{0.17em}\left(3,\hspace{0.17em}0\right)$

$y-$intercept: It is point where $x=0.$

$$\begin{gathered} 2\left(0\right)+3y=6 \\ 3y=6 \\ y=\frac{6}{3} \\ y=2 \end{gathered}$$

$\mathrm{Y}\hspace{0.17em}\mathrm{Intercepts}:\hspace{0.17em}\left(0,\hspace{0.17em}2\right)$