SOLUTION: what is (12, 5) and (-4, 1)

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Question 140614: what is (12, 5) and (-4, 1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to find the equation through these points?


First lets find the slope through the points (12,5) and (-4,1)

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 (12,5) and is the second point (-4,1))

m=%281-5%29%2F%28-4-12%29 Plug in y%5B2%5D=1,y%5B1%5D=5,x%5B2%5D=-4,x%5B1%5D=12 (these are the coordinates of given points)

m=+-4%2F-16 Subtract the terms in the numerator 1-5 to get -4. Subtract the terms in the denominator -4-12 to get -16


m=1%2F4 Reduce

So the slope is
m=1%2F4

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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-5=%281%2F4%29%28x-12%29 Plug in m=1%2F4, x%5B1%5D=12, and y%5B1%5D=5 (these values are given)


y-5=%281%2F4%29x%2B%281%2F4%29%28-12%29 Distribute 1%2F4

y-5=%281%2F4%29x-3 Multiply 1%2F4 and -12 to get -12%2F4. Now reduce -12%2F4 to get -3

y=%281%2F4%29x-3%2B5 Add 5 to both sides to isolate y

y=%281%2F4%29x%2B2 Combine like terms -3 and 5 to get 2
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Answer:


So the equation of the line which goes through the points (12,5) and (-4,1) is:y=%281%2F4%29x%2B2

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F4 and the y-intercept is b=2

Notice if we graph the equation y=%281%2F4%29x%2B2 and plot the points (12,5) and (-4,1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%281%2F4%29x%2B2 through the points (12,5) and (-4,1)

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