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

Question

anonymous · Answer

For Line L: 
$$y=mx+b$$ You're given the y-intercept which is the -5, so
$$y=mx-5$$ Use the other point on L to get the gradient (m) but substituting in the point for x & y, & solve to get m:
$$-2=m*6-5$$$$-2 = 6m-5$$$$-2+5=6m$$$$3=6m$$$$m=1/2$$Given that the line P is perpendicular to the line L, the gradient of line P must be -2 (opposite sign & reciprocal value to line L), so equation of Line P: $$y=-2x+b$$substitute the point you're given (that is (-5,0) to find the required value for b, which is the y-intercept of the line P.  you get$$0=-2*-5 + b$$$$0=10+b$$$$b=-10$$Line P is $$y=-2x-10$$To find the intersection, equate the two lines and solve to find x$$x/2-5 = -2x-10$$$$x-10 = -4x-20$$$$5x = -10$$$$x=-2$$