Answer:
[tex]y=\frac{1}{2} x+8[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
Perpendicular lines will always have slopes that are negative reciprocals of each other. For example, two perpendicular lines might have slopes of 3 and -1/3.
After observing the equation y=-2x-5, we can conclude that the slope is -2. Therefore, a line perpendicular to this line would have a slope of 1/2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2} x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2} x+b[/tex]
Plug in the given point (-4,6)
[tex]6=\frac{1}{2}(-4)+b\\6=-2+b[/tex]
Add 2 to both sides
[tex]6+2=-2+b+2\\8=b[/tex]
Therefore, the y-intercept is 8. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]:
[tex]y=\frac{1}{2} x+8[/tex]
I hope this helps!
