Answer
Point-slope form is $y+4=-\frac{3}{5}\left( x-10 \right)$.
Slope-intercept form is $y=-\frac{2}{3}x+2$.
Work Step by Step
For a line with slope m and passing through the point $\left( {{x}_{1}},{{y}_{1}} \right)$ , the point slope form is given as:
$y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$
Consider $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 10,-4 \right)$
Change the values of m and $\left( {{x}_{1}},{{y}_{1}} \right)$ as:
$\begin{align}
& y-\left( -4 \right)=-\frac{3}{5}\left( x-10 \right) \\
& y+4=-\frac{3}{5}\left( x-10 \right) \\
& y+4=-\frac{3}{5}x+6
\end{align}$
Subtract $4$ from both sides of the above equation:
$\begin{align}
& y=-\frac{3}{5}x+6-4 \\
& =-\frac{3}{5}x+2
\end{align}$
The point-slope form of a line is $y=-\frac{3}{5}x+2$.
The slope-intercept form of the equation of a line is given by $y=mx+b$ ; here, m is the slope and b is the y-intercept, and the y-intercept is the y-coordinate of a point where the line intersects the y-axis.
Change the values of m and $\left( x,y \right)=\left( 10,-4 \right)$ in $y=mx+b$ to find the value of b:
$\begin{align}
& -4=-\frac{3}{5}\left( 10 \right)+b \\
& b=2
\end{align}$
Now, change the values of b and m in $y=mx+b$.
Thus
$y=-\frac{3}{5}x+2$
The slope-intercept form of the line is $y=-\frac{3}{5}x+2$.
Therefore, the point-slope form with $m=-\frac{3}{5}$ and passing through the point $\left( 10,-4 \right)$ is $y+4=-\frac{3}{5}\left( x-10 \right)$ , and the slope-intercept form is $y=-\frac{3}{5}x+2$.
