Write an equation of the line passing through P and perpendicular to the given line. P(2,8) y=2x+1

Answer 1

When determining whether or not two lines are parallel or perpendicular, you need to use the slope. Fortunately, your problem provides the equation of the line in slope-intercept form. y=mx+b, where m is the slope of the line and b is the y-intercept.

For parallel lines the slope will be the same.

For a perpendicular line, the slope will be the negative reciprocal, for example, a slope of -2 would become 1/2 or 1/4 would become -4.

In this case, the slope of 2 would become -1/2.

Your partial equation can be set up now

y=1/2x+b

How do we get b? We can now use the point provided, (2,8)

Our x value is 2, and our y value is 8. We can solve for b.

(8)=-1/2(2)+b

We can use algebra and simplify this to:

1. 8=-1+b
2. b=9

Therefore, our new, full equation would be:

y=-1/2x+9