Question

PLEASE PLEASE PLEASE PLEASE HELP WITH MATH. ILL GIVE POINTS, BRAINY, AND FRIEND.

If given an equation of a line such as y = -1/2x + 6, demonstrate on the whiteboard how to create an equation of a line parallel and perpendicular to this line that goes through another point such as (4, 10).

Answer 1

Parallel line = Same m value (same slope)

Perpendicular line = The reciprocal m value (x/y = y/x).

Going through a point = First, find the slope of the line (perpendicular or parallel), then plug in the point (4,10) to find the y intercept.

Answer 2

See below.

Explanation:

Parallel

y = -1/2x + b

The slope is the same for any set of parallel lines. The point determines the y intercept.

x = 4

y = 10

Solve for b

10 = -1/2(4) + b

10 = - 2 + b

b = 10 + 2

b = 12

Equation: y = - 1/2 x + 12

Perpendicular

Here you actually have to solve for the slope.

Equation

m1 * m2 = - 1

m1 is the given slope of - 1/2 which I will chance to -0.5. Substitute for m1.

-0.5 * m2 = - 1 Divide by -0.5

m2 = -1/-0.5

m2 = 2

Now what you have is

y = 2x + b

x = 4

y = 10

10 = 2*4 + b

10 = 8 + b

10 - 8 = b

b = 2

Equation: y = 2x + 2