Answer
True
Work Step by Step
The given equation of line is
$y=-\frac{2}{5}x-4$
This is in the standard form of slope-intercept.
$y=mx+c$,
where $m$ is a slope of the line.
We have $m_1=−\frac{2}{5}$.
Two lines are perpendicular if their slopes are negative reciprocal to each other.
Hence, slope of the perpendicular line $m_2=−\frac{1}{m_1}$
$m_2=−\frac{1}{−\frac{2}{5}}$
Simplify.
$m_2=\frac{5}{2}$
If the line passes through a point $(x_1,y_1)$ then point-slope form of the perpendicular line's equation is.
$\Rightarrow y−y_1=m_2(x-x_1)$
We have the point $(x_1,y_1)=(-3,-1)$.
Plug all values into the point-slope form.
$\Rightarrow y-(-1)=(\frac{5}{2})(x-(-3))$
Simplify.
$\Rightarrow y+1=(\frac{5}{2})(x+3)$
Use distributive property.
$\Rightarrow y+1=\frac{5}{2}x+\frac{15}{2}$
Multiply the equation by $2$.
$\Rightarrow 2(y+1)=2\left (\frac{5}{2}x+\frac{15}{2} \right )$
Simplify.
$\Rightarrow 2y+2=5x+15$
Add $-2y-15$ to both sides.
$\Rightarrow 2y+2-2y-15=5x+15-2y-15$
Simplify.
$\Rightarrow -13=5x-2y$
Rearrange.
$\Rightarrow 5x-2y=-13$.
The given statement is true.
