Answer:
The equation of the line is:
[tex]y = -\frac{1}{2}x + 3[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Perpendicular lines:
If two lines are perpendicular, this means that the multiplication of their slopes is -1.
Perpendicular to y=2x+7
This means that:
[tex]2m = -1[/tex]
[tex]m = -\frac{1}{2}[/tex]
So
[tex]y = -\frac{1}{2}x + b[/tex]
Passing through the point (-4,5)
This means that when [tex]x = -4, y = 5[/tex]. We use this to find b.
[tex]y = -\frac{1}{2}x + b[/tex]
[tex]5 = -\frac{1}{2}(-4) + b[/tex]
[tex]2 + b = 5[/tex]
[tex]b = 3[/tex]
The equation of the line is:
[tex]y = -\frac{1}{2}x + 3[/tex]
