Answer
Graph of $-4x+y\le5$
Work Step by Step
First, graph the equation $
-4x+y=5
$.
To find points on the equation, $
-4x+y=5
$, substitute values of $x$ and solve for the corresponding value of $y$. That is,
\begin{array}{l|r}
\text{If }x=0: & \text{If }x=1:
\\\\
-4(0)+y=5 & -4(1)+y=5
\\
0+y=5 & -4+y=5
\\
y=5 & y=5+4
\\
& y=9
.\end{array}
Thus, the points $
(0,5)
$ and $
(1,9)
$ are points on the line determined by the equation $
-4x+y=5
$.
The graph of $-4x+y\le5$ is the area on and above or below the line $-4x+y=5$. To determine if it is above or below the line, use a test point, such as $(0,0)$. That is,
\begin{align*}\require{cancel}
-4(0)+0&\overset{?}\le5
\\
0+0&\overset{?}\le5
\\
0&\overset{\checkmark}\le5
.\end{align*}
Since the substitution above ended with a true statement, then the graph is the area that includes the test point.
