Question

in the xy-plane with coordinates (0, -5) and (6, -2) lie on line L. Line P contains the point with coordinates (-5,0) and is perpendicular to line L. What is the x-coordinate of the point where lines L and P intersect

Answer 1

Find equation of line L first by finding its slope. Write it in y = mx + b (slope intercept form.

Answer 2

would it be y=1/2x-5 ?

Answer 3

Sounds good to me. :) Excellent.
Now, let us find the slope of the line perpendicular to this line.

Answer 4

use the two points to find the slope for L
m = slope = rise/run
then use:
y-y1=m(x-x1) with one of the points, this will be your first equation
. your second equation, since it is perpendicular, the slope will be the negative reciprocal of the first.
use the above formula for finding the equation of the line again with this new slope
once you have the two equations of the lines equate them to eachother and solve for x, this will be where they equal eachother

Answer 5

What would be the slope of the line perpendicular to L? Remember, slope of line L is 1/2 based on your calculations.

Answer 6

the slope of line P would be -2... i equated the two equations and got x=-2

Answer 7

Yes, slope of P = -2. So, line P is:
y = -2x + b

b = ? given this line goes through (-5,0)

Answer 8

b= -10...would the point of intersection be (-2, -10)?

Answer 9

y = -2x - 10
y = x/2 - 5

Does -2, -10 satisfy both equations? If so, that is the right answer.

Answer 10

x/2 - 5 = -2x - 10
5x/2 = -10 + 5
5x/2 = -5
x = -2

y = -2/2 - 5 = -1 -5 = -6

So, it appears like (-2, -6) is the right intersection point.

Answer 11

ok i understand that part. but what was the point in finding b?

Answer 12

Well, that is how you can find the "full" equation of the line.

Answer 13

ok i see. thanks for your help