# How do you graph 5x-2y=10?

Mar 31, 2017

See the explanation.

#### Explanation:

Graph:

$5 x - 2 y = 10$

This equation is in standard form for a linear equation. You only need two points to graph a straight line. The standard form makes it easy to find the x- and y-intercepts, which can be graphed.

$5 x - 2 y = 10$

X-intercept: value of $x$ when $y = 0$.

Substitute $0$ fro $y$ and solve for $x$.

$5 x - 2 \left(0\right) = 10$

$5 x = 10$

Divide both sides by $5$.

$x = \frac{10}{5}$

$x = 2$

The x-intercept is $\left(2 , 0\right)$.

Y-intercept: value of $y$ when $x = 0$

Substitute $0$ for $x$ and solve for $y$.

$5 \left(0\right) - 2 y = 10$

$- 2 y = 10$

Divide both sides by $- 2$.

$y = \frac{10}{-} 2$

$y = - 5$

The y-intercept is $\left(0 , - 5\right)$

Plot the x- and y-intercepts and draw a straight line through the points.

graph{5x-2y=10 [-16.23, 15.8, -10.26, 5.76]}

Mar 31, 2017

Find the $x \mathmr{and} y$- intercepts and draw a line through them.

#### Explanation:

If you are given the equation of a straight line in standard form
$\left(a x + b y = c\right)$, then you can find the $x \mathmr{and} y$-intercepts.

To find the $x$-intercept, make $\textcolor{red}{y = 0}$

$5 x - 2 \textcolor{red}{y} = 10 \text{ "rarr5x-2color(red)((0)) = 10" }$ Solve for $x$
$5 x = 10$

$x = 2 \text{ } \leftarrow$ this is the $x$-intercept

To find the $y$-intercept, make $\textcolor{b l u e}{x = 0}$

$5 \textcolor{b l u e}{x} - 2 y = 10 \text{ "rarr5color(blue)((0))-2y = 10" }$ Solve for $y$
$- 2 y = 10$

$y = - 5 \text{ } \leftarrow$ this is the $y$-intercept

Now you can plot the two intercepts on a grid and draw a line passing through both of them. graph{5x-2y = 10 [-6.06, 13.94, -8.06, 1.94]}