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?

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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?

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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\[x/2-5 = -2x-10\]\[x-10 = -4x-20\]\[5x = -10\]\[x=-2\]

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