Answer: [tex]y=2x+7[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" the y-intercept.
Given the equation:
[tex]y=-\frac{1}{2}x-4[/tex]
You can identify that:
[tex]m=-\frac{1}{2}[/tex]
Since the slopes of perpendicular lines are negative reciprocals, the slope of the line perpendicular to [tex]y=-\frac{1}{2}x-4[/tex] must be:
[tex]m=2[/tex]
Substitute the slope and the coordinates of the given point into [tex]y=mx+b[/tex] and solve for "b":
[tex]3=(2)(-2)+b\\\\3+4=b\\\\b=7[/tex]
Therefore, the equation of that line is:
[tex]y=2x+7[/tex]
