Answer
a) $y=\frac{6}{5}x-4$
b) $m=6/5$, $b=-4$
c) See below.
Work Step by Step
(a)
Rearrange the equation in the standard slope-intercept form of $y=mx+c$ by solving the equation for y. Bring all the variables other than y and constant terms to one side.
$\begin{align}
& 6x-5y-20=0 \\
& y=\frac{6}{5}x-4
\end{align}$
The slope intercept form of the equation is $y=\frac{6}{5}x-4$.
(b)
From (a) above, the slope-intercept form of the equation is $y=\frac{6}{5}x-4$.
Compare the given equation with the standard slope-intercept form of the equation, $y=mx+c$ where m is the slope and c is the y-intercept of the equation.
From the given equation $m=\frac{6}{5}$ and $c=-4$.
Hence, the slope of equation is $\frac{6}{5}$ and y-intercept is $-4$.
The slope of the equation $6x-5y-20=0$ is $\frac{6}{5}$ and y-intercept is $-4$.
(c)
From (b) above, we have $m=\frac{6}{5}$ and $c=-4$.
Now,
$\begin{align}
& \text{slope=}\frac{\text{rise}\left( \text{Change}\,\text{in}\,\text{y} \right)}{\text{run}\left( \text{Change}\,\text{in}\,\text{x} \right)} \\
& m=\frac{6}{5}
\end{align}$
Therefore,
$\begin{align}
& \text{rise}=6 \\
& \text{run}=5
\end{align}$
Here, rise means the change in the y-axis and run means the change in the x-axis.
The y-intercept is $c=-4$, so $\left( 0,-4 \right)$ will be one of its points.
Plot $\left( 0,-4 \right)$ on the graph and increase y by rise and x by run to plot the other point.
Join these points to get the line of equation $6x-5y-20=0$:
