SOLUTION: 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, -12

Question 170382: 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 checkley77(12844) (Show Source): You can put this solution on YOUR website!
(3,9),(5,13),(15,33),(34,71),(678,1359), and (1234,2471) all lie on line M.
First we find the slope=(y2-y1)/(x2-x1)
Slope=(13-9)/(5-3)=4/2=2 for this slope.
Now replace one set of (x,y) values in the line equation Y=mX+b & solve for the y intercept (b).
9=2*3+b
9=6+b
b=9-6
b=3 the y intercept for line M.
Thus the equation for this line M is:
y=2x+3 Equaton for line M (red line)
--------------------------------------
(3,-9),(5,-11),(15,-21),(34,-40),(678,-684), and (1234,-1240) all lie on line N.
Doing the for these points & line:
slope=(-11+9)/(5-3)=-2/2=-1 for this slope.
-9=-1*3+b
-9=-3+b
b=-9+3
b=-6 the y intercept.
Thus the equation for this line is:
y=-x-6 Equation for line N (green line)
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2x +3 and -x -6).
Intercept=(-3,-3)
X axis intercept for M=-1.5, for N=-6
Y axis intercept for M=3, for N=-6

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