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

Given function

$x + 5 y = 5$

$\setminus \frac{x}{5} + \setminus \frac{5 y}{5} = 1$

$\frac{x}{5} + \frac{y}{1} = 1$

The above line has x-intercept $= 5$

y-intercept $= 1$

i,e, the line intersects the coordinate axes at the points $\left(5 , 0\right)$ & $\left(0 , 1\right)$

Now, specify the points $\left(5 , 0\right)$ & $\left(5 , 0\right)$ & join these points to get plot of given straight line

Jul 3, 2018

#### Explanation:

First find the $x$-intercept by putting $y = 0$ i.e. $x = 5$, which gives us point $\left(5 , 0\right)$

then find $y$-intercept by putting $x = 0$ i.e. $5 y = 5$ or $y = \frac{5}{5} = 1$, giving us another point $\left(0 , 1\right)$.

Joining two points gives us the graph of $x + 5 y = 5$, as shown below

graph{(x+5y-5)(x^2+(y-1)^2-0.01)((x-5)^2+y^2-0.01)=0 [-3.42, 6.58, -1.42, 3.58]}

Jul 3, 2018

Use two arbitrary values for $x$. For example, find the intercept with $y$ if $x = 0$.

$0 + 5 y = 5$
$5 y \textcolor{red}{/ 5} = 5 \textcolor{red}{/ 5}$
$y = 1$

Now you know one of the intercepts is $\left(0 , 1\right)$. Continue using another random $x$ value. Let's try $x = 5$.

$\cancel{5 \textcolor{red}{- 5}} + 5 y = 5 \textcolor{red}{- 5}$
$5 y \textcolor{red}{/ 5} = 0 \textcolor{red}{/ 5}$
$y = 0$

The second intercept is $\left(5 , 0\right)$.

Using these two intercepts, you can map out an x-axis and y-axis on some graph paper; draw these two intercepts and connect a line through them.

Jul 3, 2018

As below

#### Explanation:

$x + 5 y = 5$

$5 y = - x + 5$

$y = - \frac{x}{5} + 1$

Y-intercept = 1

X-intercept when y = 0

$\frac{x}{5} = 1$

X-intercept = 5

Two points are (5, 0), (0, 1)

graph{-x/5 + 1 [-10, 10, -5, 5]}