Answer
\begin{align*}
\text{$x$-intercept: }&
\left(-\dfrac{5}{2}, 0\right)
\\
\text{$y$-intercept: }&
(0, 10)
\end{align*}
Work Step by Step
To find the $x$-intercept of the given equation, $
-4x+y=10
,$ substitute $y=0$ and then solve for $x.$ That is,
\begin{align*}
-4x+0&=10
\\
-4x&=10
\\\\
\dfrac{-4x}{-4}&=\dfrac{10}{-4}
\\\\
x&=-\dfrac{10}{4}
\\\\
x&=-\dfrac{5}{2}
\end{align*}
To find the $y$-intercept of the given equation, substitute $x=0$ and then solve for $y.$ That is,
\begin{align*}
-4(0)+y&=10
\\
0+y&=10
\\
y&=10
\end{align*}
Hence, the intercepts of the given equation are
\begin{align*}
\text{$x$-intercept: }&
\left(-\dfrac{5}{2}, 0\right)
\\
\text{$y$-intercept: }&
(0, 10)
\end{align*}
