Question

Graph the equation$-x+4y=8$using the intercepts.

Short answer

The graph of the given equation is

.

Step-by-step solution

Given information

The equation is given as $-x+4y=8$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.

$\begin{array}{rcl}-x+4y& =& 8\\ -x+4\left(0\right)& =& 8\\ -x& =& 8\\ x& =& -8\\ -x+4y& =& 8\\ -0+4y& =& 8\\ 4y& =& 8\\ y& =& \frac{8}{4}\\ y& =& 2\end{array}$

Graph the given equation

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

• As obtained, the intercepts of the given equation are (-8,0) and (0,2).
• Hence join the intercepts using a straight line to get the required graph of the equation.