SOLUTION: 17. A line passing through (13, 16) and (9, y) is parallel to a line with slope 2. What is the value of y?

Algebra ->  Coordinate-system -> SOLUTION: 17. A line passing through (13, 16) and (9, y) is parallel to a line with slope 2. What is the value of y?      Log On


   

Question 110378: 17. A line passing through (13, 16) and (9, y) is parallel to a line with slope 2. What is the value of y?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (13,16) and is the second point (9,y))

2=%28y-16%29%2F%289-13%29 Plug in y%5B2%5D=y,y%5B1%5D=16,x%5B2%5D=9,x%5B1%5D=13 (these are the coordinates of given points). Now plug in m=2 (this is the given slope)

2=+%28y-16%29%2F-4 Subtract the terms in the denominator 9-13 to get -4


-8=y-16 Multiply both sides by -4


8=y Add 16 to both sides



So the value of y is y=8



Notice if we find the slope of (13,16) and (9,8), we get


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (13,16) and is the second point (9,8))

m=%288-16%29%2F%289-13%29 Plug in y%5B2%5D=8,y%5B1%5D=16,x%5B2%5D=9,x%5B1%5D=13 (these are the coordinates of given points)

m=+-8%2F-4 Subtract the terms in the numerator 8-16 to get -8. Subtract the terms in the denominator 9-13 to get -4


m=2 Reduce

So the slope is
m=2


So our answer is verified