Question

How do you graph $x-2y=1$ using the intercepts?

Answer 1

We can draw the graph using intercepts concept. First we have to find the $x$ and $y$ intercepts. we have to make $x$ as $0$ while calculating y intercept and we have to make $y$ as $0$ while calculating $x$ intercept. By solving this we can get the $x$ and $y$ intercepts to draw the graph.

Complete step by step answer:
Given equation is
$x-2y=1$
Now we have to find the $x$ intercept of the equation.
To find it we have to substitute the $y$ value with $0$.
By substituting it and simplifying it we will get the $x$ intercept .
Now we are going to substitute $y=0$ in the equation.
We will get
$\Rightarrow x-2\left( 0 \right)=1$
$\Rightarrow x-0=1$
From this we can write
$\Rightarrow x=1$
So the $x$ intercept of the equation is $1$
The point to plot on the graph is $\left( 1,0 \right)$
Now we have to find the $y$ intercept of the equation.
To find it we have to substitute the $x$ value with $0$.
By substituting it and simplifying it we will get the $y$ intercept .
Now we are going to substitute $x=0$ in the equation.
We will get
$\Rightarrow 0-2y=1$
$\Rightarrow -2y=1$
We have to divide the equation with $2$ on both sides
From this we can write
$\Rightarrow \dfrac{-2y}{2}=\dfrac{1}{2}$
By simplifying it we will get
$\Rightarrow -y=0.5$
To find the value of $y$ we have to multiply the equation with the$-$ sign.
We will get
$\Rightarrow y=-0.5$
So the $y$ intercept of the equation is $-0.5$
The point to plot on the graph is $\left( 0,-0.5 \right)$
So the intercepts of $x$ and $y$ are $1$ and $-0.5$ respectively.
Now we have to plot the graph it will look like

Note: We can also take different values for $x$ and $y$ and plot the graph. But here it is mentioned as an intercept we are taking the values as $0$ otherwise we can take the values of our own choice and draw the graph.