The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the line
[tex]y-2=-\dfrac{1}{4}(x+3)\to m=-\dfrac{1}{4}[/tex]
If m₁ and m₂ are the slopes of the perpendicular lines, then
[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
Therefore the slope of ouer line is
[tex]m=-\dfrac{1}{-\frac{1}{4}}=4[/tex]
We have the point (-3, 5). Put the coordinates to the equation of a line in the point-slope form:
[tex]y-5=4(x-(-3))\\\\\boxed{y-5=4(x+3)}[/tex]
