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. Form the equations of both t
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Question 179107: 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. Form the equations of both the lines and show your work.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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. Form the equations of both the lines and show your work.
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Only 2 points are needed to define a line. Pick any 2.
For M use (1,3) and (2,5)
|x y 1|
|1 3 1| = 0
|2 5 1|
x*(3-5) - y*(1-2) + 5-6 = 0
-2x + y -1 = 0
2x-y = -1
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For N use (1,-1) and (2,-3)
|x y 1|
|1 -1 1| = 0
|2 -3 1|
x*(-1+3) - y*(1-2) + -3 + 2 = 0
2x + y = 1
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The equation of a line passing through two points is given by the two-point form:
)
Select two points from the first set of points:
)
and )
Substitute the given coordinates:
)
Perform the indicated arithmetic:
)
Solve for y to get the slope-intercept form:
Now, since you were given all of those other points, and you weren't told that line M is a straight line, you need to insert the coordinates of all the other points, one point at a time, into this equation to verify that they are all actually on this line. Simply put, verify that each y-coordinate is two times the x-coordinate plus 1.
Next, repeat the process for the other set of points to create your other equation.
John
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