# How do you find the intercepts for 4x+3y=8?

Mar 25, 2018

$x$-intercept$\left(2 , 0\right)$
$y$-intercept$\left(0 , \frac{8}{3}\right)$

#### Explanation:

To find the $x$-intercept, substitute $y = 0$,

$4 x = 8$
$x = 2$

To find the $y$-intercept, substitute $x = 0$,

$3 y = 8$
$y = \frac{8}{3}$

Hence, the $x$-intercepts and $y$-intercepts are $\left(2 , 0\right)$ and $\left(0 , \frac{8}{3}\right)$ respectively.

Mar 25, 2018

The graph intersects the $X$ axis in ${P}_{1} \left(2 , 0\right)$ and the $Y$ axis in ${P}_{2} \left(0 , \frac{8}{3}\right)$.

#### Explanation:

The graph intersects the $Y$ axis when $X = 0$ and the $X$ axis when $Y = 0$. Therefore, taking $4 x + 3 y = 8$ and the cases:

1. When $x = 0$:
$3 y = 8 \implies y = \frac{8}{3}$
${P}_{2} \left(0 , \frac{8}{3}\right)$

2. When $y = 0$:
$4 x = 8 \implies x = \frac{8}{4} = 2$
${P}_{1} \left(2 , 0\right)$

graph{4x+3y=8 [-7.024, 7.02, -3.51, 3.51]}