SOLUTION: 15. Find the slope of the line passing through the points (14, 6) and (9, 1).

Algebra ->  Graphs -> SOLUTION: 15. Find the slope of the line passing through the points (14, 6) and (9, 1).      Log On


   

Question 102638: 15. Find the slope of the line passing through the points (14, 6) and (9, 1).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (14,6) and (9,1)

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 (14,6) and is the second point (9,1))

m=%281-6%29%2F%289-14%29 Plug in y%5B2%5D=1,y%5B1%5D=6,x%5B2%5D=9,x%5B1%5D=14 (these are the coordinates of given points)

m=+-5%2F-5 Subtract the terms in the numerator 1-6 to get -5. Subtract the terms in the denominator 9-14 to get -5


m=1 Reduce

So the slope is
m=1

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-6=%281%29%28x-14%29 Plug in m=1, x%5B1%5D=14, and y%5B1%5D=6 (these values are given)


y-6=1x%2B%281%29%28-14%29 Distribute 1

y-6=1x-14 Multiply 1 and -14 to get -14

y=1x-14%2B6 Add 6 to both sides to isolate y

y=1x-8 Combine like terms -14 and 6 to get -8
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Answer:


So the equation of the line which goes through the points (14,6) and (9,1) is:y=1x-8

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1 and the y-intercept is b=-8

Notice if we graph the equation y=1x-8 and plot the points (14,6) and (9,1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=1x-8 through the points (14,6) and (9,1)

Notice how the two points lie on the line. This graphically verifies our answer.