Answer:
[tex]\sf y=\dfrac12x-3[/tex]
Step-by-step explanation:
If two lines are perpendicular, the product of their slopes is -1.
The slope of the given equation is -2, so the slope of the line perpendicular to it is [tex]\sf \dfrac12[/tex] as [tex]\sf -2 \times \dfrac12=-1[/tex]
Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]
(where m is the slope and [tex]\sf (x_1,y_1)[/tex] is a point on the line)
Given:
Substitute the given values into the formula:
[tex]\sf \implies y-(-5)=\dfrac12(x-(-4))[/tex]
[tex]\sf \implies y+5=\dfrac12x+2[/tex]
[tex]\sf \implies y=\dfrac12x-3[/tex]
Compare to slope intercept form y=mx+b
Slope of the Perpendicular line 1/2
Equation in point slope form
[tex]\\ \rm\rightarrowtail y+5=1/2(x+4)[/tex]
[tex]\\ \rm\rightarrowtail y=1/2x+2-5[/tex]
[tex]\\ \rm\rightarrowtail y=1/2x-3[/tex]
