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
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Find equation of line L first by finding its slope. Write it in y = mx + b (slope intercept form.
would it be y=1/2x-5 ?
Sounds good to me. :) Excellent.
Now, let us find the slope of the line perpendicular to this line.
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use the two points to find the slope for L
m = slope = rise/run
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
What would be the slope of the line perpendicular to L? Remember, slope of line L is 1/2 based on your calculations.
the slope of line P would be -2... i equated the two equations and got x=-2
Yes, slope of P = -2. So, line P is:
y = -2x + b
b = ? given this line goes through (-5,0)
b= -10...would the point of intersection be (-2, -10)?
y = -2x - 10
y = x/2 - 5
Does -2, -10 satisfy both equations? If so, that is the right answer.
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.
ok i understand that part. but what was the point in finding b?
Well, that is how you can find the "full" equation of the line.