Answer
graph of $5x-2y=-4$
Work Step by Step
In the form $y=mx+b,$ the given equation, $
5x-2y=-4
,$ is equivalent to
\begin{align*}
5x-2y-5x&=-5x-4
\\
-2y&=-5x-4
\\\\
\dfrac{-2y}{-2}&=\dfrac{-5x-4}{-2}
\\\\
y&=\dfrac{5}{2}x+2
.\end{align*}
Using $y=mx+b$ or the Slope-Intercept Form of linear equations, where $b$ is the $y$-intercept and $m$ is the slope, the equation above has the following characteristics:
\begin{align*}
\text{$y$-intercept: }&
2
\\
\text{Slope: }&
\dfrac{5}{2}
.\end{align*}
To graph the slope-intercept equation above, start at the $y$-intercept. This corresponds to the point $
(0,2)
$.
Using the notion of the slope as $\dfrac{rise}{run},$ then $rise=
5
$ and $run=
2
.$
From the $y$-intercept, go $\text{
up
}$ by $rise=
5
$ units and then go to the right by $run=
2
$ units.
This results to the point $
(2,7)
.$
Connecting this point and the $y$-intercept gives the graph of the given equation.