Answer
graph of $-2x+5y=-10$
Work Step by Step
In the form $y=mx+b,$ the given equation, $
-2x+5y=-10
,$ is equivalent to
\begin{align*}
-2x+5y+2x&=-10+2x
\\
5y&=2x-10
\\\\
\dfrac{5y}{5}&=\dfrac{2x-10}{5}
\\\\
y&=\dfrac{2}{5}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{2}{5}
.\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=
2
$ and $run=
5
.$
From the $y$-intercept, go $\text{
up
}$ by $rise=
2
$ units and then go to the right by $run=
5
$ units.
This results to the point $
(5,0)
.$
Connecting this point and the $y$-intercept gives the graph of the given equation.