SOLUTION: I am asking for help with this. I am having trouble with it. 3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M. The points (3,

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Question 163816: I am asking for help with this. I am having trouble with it.
3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a. Form the equations of both the lines. Show your work.
b. What are the co-ordinates of the point of intersection of lines M and N?
c. Write the co-ordinates of the intersections of lines M and N with the x-axis.
d. Write the co-ordinates of the intersection of lines M and N with the y-axis.

Answer by scott8148(5895) (Show Source):
You can put this solution on YOUR website!
a. M __ slope is (13-9)/(5-3) __ 4/2 __ 2
__ using point-slope __ y-9=2(x-3) __ y-9=2x-6 __ y=2x+3

N __ slope is (-11-(-9))/(5-3) __ -2/2 __ -1
__ using point-slope __ y-(-9)=-1(x-3) __ y+9=-x+3 __ y=-x-6

b. at the point of intersection, the x's and y's of both equations are the same
__ 2x+3=-x-6 __ 3x=-9 __ x=-3
__ substituting to find y __ y=2(-3)+3 __ y=-3
__ intersection is (-3,-3)

c. at x-intercept, y=0
__ M __ 0=2x+3 __ -3=2x __ -3/2=x __ x-intercept is (-3/2,0)
__ N __ 0=-x-6 __ 6=-x __ -6=x __ x-intercept is (-6,0)

d. at y-intercept, x=0
__ M __ y=2(0)+3 __ y=+3 __ y-intercept is (0,3)
__ N __ y=-(0)-6 __ y=-6 __ y-intercept is (0,-6)