Answer:
[tex]y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=-4x-5[/tex]
If two lines are perpendicular to each other, their slopes are negative reciprocals.
The slope of the given equation is -4.
Therefore, the slope of the perpendicular line is ¹/₄.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-2, 3) into the point-slope formula to create the equation of the perpendicular line.
[tex]\implies y-3=\dfrac{1}{4}(x-(-2))[/tex]
[tex]\implies y-3=\dfrac{1}{4}(x+2)[/tex]
[tex]\implies y-3=\dfrac{1}{4}x+\dfrac{1}{2}[/tex]
[tex]\implies y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]
