Answer
graph of $-\dfrac{2}{9}x-\dfrac{5}{9}y=10$:
Work Step by Step
The $x$-intercept is the value of $x$ when $y=0.$ Setting $y=0$ in the given equation, $
-\dfrac{2}{9}x-\dfrac{5}{9}y=10
,$ results to
\begin{align*}
-\dfrac{2}{9}x-\dfrac{5}{9}(0)&=10
\\\\
-\dfrac{2}{9}x-0&=10
\\\\
-\dfrac{2}{9}x&=10
\\\\
\left(-\dfrac{9}{2} \right)\left(-\dfrac{2}{9}x\right)&=(10)\left(-\dfrac{9}{2} \right)
\\\\
x&=-\dfrac{90}{2}
\\\\
x&=-45
.\end{align*}
Hence, the $x$-intercept is $(
-45,0
)$.
The $y$-intercept is the value of $y$ when $x=0.$ Setting $x=0$ in the given equation results to
\begin{align*}
-\dfrac{2}{9}(0)-\dfrac{5}{9}y&=10
\\\\
0-\dfrac{5}{9}y&=10
\\\\
-\dfrac{5}{9}y&=10
\\\\
\left(-\dfrac{9}{5}\right)\left(-\dfrac{5}{9}y\right)&=(10)\left(-\dfrac{9}{5}\right)
\\\\
y&=-\dfrac{90}{5}
\\\\
y&=-18
.\end{align*}
Hence, the $y$-intercept is $(
0,-18
)$.
By connecting the two intercepts, the graph of the given line is determined.
