Question

Graph the equation $x+2y=4$using the intercepts.

Short answer

The graph of the given equation is

.

Step-by-step solution

Given information

The equation is given as $x+2y=4$to get 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.

$\begin{array}{rcl}x+2y& =& 4\\ x+2\left(0\right)& =& 4\\ x& =& 4\\ x+2y& =& 4\\ 0+2y& =& 4\\ 2y& =& 4\\ y& =& \frac{4}{2}\\ y& =& 2\end{array}$

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 (4,0) and (0,2).
• Hence join the intercepts using a straight line to get the required graph of the equation.