Answer
$A=-\frac{3}{7}$.
Work Step by Step
The given equation of the line is
$\Rightarrow Ax+y=2$
Isolate $y$.
$y=-Ax+2$
This is in the standard slope-intercept form.
Slope $m_1=-A$.
The slope of the line passing through the points $(1,-3)$ and $(-2,4)$ is:
$\Rightarrow m_2=\frac{change \; in \; y}{change \; in \; x}$
$\Rightarrow m_2=\frac{4-(-3)}{-2-1}$
$\Rightarrow m_2=\frac{4+3}{-3}$
$\Rightarrow m_2=-\frac{7}{3}$
Two lines are perpendicular if their slopes are negative reciprocal to each other.
Hence, we have:
$\Rightarrow m_1=−\frac{1}{m_2}$
Substitute all values.
$\Rightarrow -A=−\frac{1}{-\frac{7}{3}}$
Simplify.
$\Rightarrow -A=\frac{3}{7}$
$\Rightarrow A=-\frac{3}{7}$.
