Answer
Calculate the intercepts of the graph and locate the points. Connect the two points by a straight line.
Work Step by Step
Consider the general form of a line’s equation
$Ax+By+C=0$
Follow the steps given below to graph the equation using intercepts.
Step 1: Calculate the $x$ intercept.
Substitute $y=0$ in the given equation $Ax+By+C=0$ and find the value of $x$
$\begin{align}
& Ax+B\times 0+C=0 \\
& Ax=-C \\
& x=-\frac{C}{A}
\end{align}$
So, the line passes through the point $\left( -\frac{C}{A},0 \right)$.
Step 2: Calculate the $y$ intercept.
Substitute $x=0$ in the given equation $Ax+By+C=0$ and calculate the value of $y$
$\begin{align}
& A\times 0+By+C=0 \\
& By=-C \\
& y=-\frac{C}{B}
\end{align}$
So, the line passes through the point $\left( 0,-\frac{C}{B} \right)$.
Step 3: Graph the equation of the line.
Locate two intercepts $\left( -\frac{C}{A},0 \right)$ and $\left( 0,-\frac{C}{B} \right)$. Connect them by a straight line to graph the given equation $Ax+By+C=0$.
Example:
Consider the given linear equation
$2x+3y+6=0$
Follow the steps given below to graph the equation using intercepts:
Step 1: Calculate the $x$ intercept.
Substitute $y=0$ in the given equation $2x+3y+6=0$ and find the value of $x$
$\begin{align}
& 2x+3\times 0+6=0 \\
& 2x=-6 \\
& x=\frac{\left( -6 \right)}{2} \\
& =-3
\end{align}$
So, the $x$ intercept of the given equation $2x+3y+6=0$ is $-3$. Hence, the line passes through $\left( -3,0 \right)$.
Step 2: Calculate the $y$ intercept.
Substitute $x=0$ in the given equation $2x+3y+6=0$ and find the value of y
$\begin{align}
& 2\times 0+3y+6=0 \\
& 3y=-6 \\
& y=\frac{\left( -6 \right)}{3} \\
& =-2
\end{align}$
So, the $y$ intercept of the given equation $2x+3y+6=0$ is $-2$. Hence, the line passes through $\left( 0,-2 \right)$.
Step 3: Graph the equation of the line.
Locate the two intercepts $\left( -3,0 \right)$ and $\left( 0,-2 \right)$ in the graph. Connect them by a straight line.
The graph of given equation $2x+3y+6=0$ is as follows:
