# How do you graph 2x+5y=10 using intercepts?

Mar 19, 2017

Graph of $y = - \frac{2}{5} x + 2$
graph{-2/5x + 2 [-7, 7, -7, 7]}

#### Explanation:

The equation of a straight line with gradient $m$ and $y$-intercept $c$ is:

$y = m x + c$

You have been given all the information you need but to get to this format, need to rearrange:

$2 x + 5 y = 10$

subtracting $2 x$ from each side gives

$- 2 x + 2 x + 5 y = 10 - 2 x$

$5 y = - 2 x + 10$

Dividing through both sides by $5$ gives

$\frac{5 y}{5} = \frac{- 2 x}{5} + \frac{10}{5}$

$y = - \frac{2}{5} x + 2$

So now it can be seen that the $y$-intercept is $2$ and the gradient is $- \frac{2}{5}$.

The $x$-intercept can be found when $y = 0$:

$0 = - \frac{2}{5} x + 2$

To find the value of $x$ this again needs rearranging:

$0 + \frac{2}{5} x = - \frac{2}{5} x + 2 + \frac{2}{5} x$

$\frac{2}{5} x = 2$

$\frac{2}{5} x \times \frac{5}{2} = 2 \times \frac{5}{2}$

$x = \frac{10}{2} = 5$

So the $x$-intercept is at $5$.

This means that the graph will cross through:

the $x$-intercept $\left(0 , 5\right)$; and

the $y$-intercept $\left(2 , 0\right)$.

You can mark these on your graph and then draw a line through them both.

Graph of $y = - \frac{2}{5} x + 2$
graph{-2/5x + 2 [-7, 7, -7, 7]}

Mar 19, 2017

see explanation.

#### Explanation:

To find the intercepts.

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

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

$x = 0 \to 0 + 5 y = 10 \to y = 2 \leftarrow \textcolor{red}{\text{ y-intercept}}$

$y = 0 \to 2 x + 0 = 10 \to x = 5 \leftarrow \textcolor{red}{\text{ x-intercept}}$

Plot the points (0 ,2) , (5 ,0) and draw a straight line through them. This is the graph of 2x + 5y = 10
graph{-2/5x+2 [-10, 10, -5, 5]}