SOLUTION: The points (1, 3), (2, 5), (8, 17), (50, 101), and (1000, 2001) all lie on line M. The points (1, -1), (2, -3), (8, -15), (50, -99), and (1000, -1999) all lie on line N. a. Form

Question 203229: The points (1, 3), (2, 5), (8, 17), (50, 101), and (1000, 2001) all lie on line M.
The points (1, -1), (2, -3), (8, -15), (50, -99), and (1000, -1999) 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. Could you help me with these? This is very difficult for me. You are very much appreciated.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Since we are talking about linear equations, we need only two points to define the line and we can write the equation of the line if we know its slope and its y-intercept.
We can write the equations in the slope-intercept form: y = mx+b where m = slope and b = y-intercept.
For line M, pick any two of the given five points to find the slope (m) of the line:
Let's pick the first two points from the list (1, 3) and (2, 5) and substitute their x- and y-cordinates into the slope formula:

so, we have, so far...
To find b, the y-intercept, you can use the x- and y-coordinates of either one of the two points (or any of the other given points for that matter, as long as they lie on the line). Let's use the first point in the list (1, 3):
Subtract 2 from both sides of the equation.
so the final equation for line M is:

Similarly, for line N:
Pick points (1, -1) and (2, -3), substitute their x- and y-coordinates:

so...
use the second point (2, -3) to find b, substitute:

Add 4 to both sides.
so the final equation for line N is:

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The point of intersection of the two lines is found by solving the system of linear equations just developed. This is esily done by setting the two equations equal and solving for x.
Add 2x to both sides.
Subtract 1 from both sides.
so...
now substitute this into either one of the two equations and solve for y:

The point of intersection of the two lines is (0, 1)
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The line intersect the x-axis at y = 0, so, set y = 0 in each equation and solve for x.
For line M:
Substitute y = o.
Subtract 1 from both sides.
Divide both sides by 2.
or
For line N:
Substitute y = 0.
Subtract 1 from both sides.
Divide both sides by -2.
or
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Remember that the intersection of the lines with the y-axis is called the y-intercept or b in the equation of the lines.
Foe line M: b = 1.
For line N: b = 1.
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