# How do you graph -8x+10y=40 using intercepts?

Mar 26, 2017

see explanation.

#### Explanation:

To find the $\textcolor{b l u e}{\text{ x and y intercepts}}$

• " let x = 0, in the equation, to find y-intercept"

• " let y = 0, in the equation, to find x-intercept"

$x = 0 \to 10 y = 40 \Rightarrow y = 4 \leftarrow \textcolor{red}{\text{ y-intercept}}$

$y = 0 \to - 8 x = 40 \Rightarrow x = - 5 \leftarrow \textcolor{red}{\text{ x-intercept}}$

Plot the points (0 ,4), (-5 ,0) and draw a straight line through them for the graph.
graph{4/5x+4 [-11.25, 11.25, -5.625, 5.625]}

Mar 26, 2017

Plug in $0$ for $x$ to find the $y$-intercept, and $0$ for $y$ to find the $x$-intercept. Then, graph these two points on a coordinate plane and connect them.

See below for the solution with graph.

#### Explanation:

Keep in mind that the $x$-intercept is the point where $y$ is $0$, and the $y$-intercept is the point where $x$ is $0$.

It's easier to remember this if you think about the intercepts on a graph $-$ any point on the $y$-axis has to have an $x$ coordinate of $0$, or else it wouldn't be on the $y$-axis (and vice versa).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First, find the $x$-intercept by plugging in $0$ for $y$.

$- 8 x + 10 \left(0\right) = 40$
$\textcolor{w h i t e}{\text{XXXX--}} - 8 x = 40$
$\textcolor{w h i t e}{\text{XXXXXX..}} x = - 5$

The $x$-intercept, then, is color(red)("(-5, 0)

Next, find the $y$-intercept by plugging in $0$ for $x$.

$- 8 \left(0\right) + 10 y = 40$
$\textcolor{w h i t e}{\text{XXXXX-}} 10 y = 40$
$\textcolor{w h i t e}{\text{XXXXXX..}} y = 4$

The $y$-intercept, then, is color(blue)("(0, 4))

Finally, to graph the line, just graph these two points, and connect them, as shown below. 