Answer
$y-0=-\dfrac{7}{4}(x-0)$
Work Step by Step
With the given points, $
(0,0)$ and $(-4,7),$ then
\begin{align*}
y_1&=
0
,\\y_2&=
7
,\\x_1&=
0
,\text{ and }\\ x_2&=
-4
.\end{align*}
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope, $m,$ of the line connecting the two given points is
\begin{align*}
m&=
\dfrac{0-7}{0-(-4)}
\\\\&=
\dfrac{0-7}{0+4}
\\\\&=
\dfrac{-7}{4}
\\\\&=
-\dfrac{7}{4}
.\end{align*}
Using $
y-y_1=m(x-x_1)
$ or the Point-Slope Form, with $m=
-\dfrac{7}{4}
$ and using the point $
(0,0)
$, then
\begin{align*}
y-0=-\dfrac{7}{4}(x-0)
.\end{align*}
A Point-Slope Form of the line with the given conditions is $
y-0=-\dfrac{7}{4}(x-0)
.$
