Question

Graph the equation $3x+y=3$using the intercepts.

Short answer

The graph of the given equation is

.

Step-by-step solution

Given information

The equation is given as$3x+y=3$for the graph.

Find the intercepts

Apply the definition of the intercepts to find the intercepts of the given equation.

• The intercepts of the given equation are the points where the corresponding variables become zero.
• Hence substitute the associated variables zero into the given equation to find the required intercepts.

$\begin{array}{rcl}3x+y& =& 3\\ 3x+0& =& 3\\ 3x& =& 3\\ x& =& \frac{3}{3}\\ x& =& 1\\ 3x+y& =& 3\\ 3\left(0\right)& =& y=3\\ y& =& 3\end{array}$

Graph the equation using the intercepts

The graph of the linear equation is a straight line that passes through its intercepts.

• As obtained, the intercepts of the given equation are (1,0) and (0,3).
• Hence join the intercepts using a straight line to get the required graph of the equation.