SOLUTION: I'm not sure what I'm suppose to do.....Do I graph? ??? = Find an equation of the line containing the given pair of points (4,2) and (12,8) What is the equation of the

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Question 91109This question is from textbook
: I'm not sure what I'm suppose to do.....Do I graph?
??? = Find an equation of the line containing the given pair of points
(4,2) and (12,8) What is the equation of the line? y=

If I graph it,is y=8??? Thanks
Cristina This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (4,2) and (12,8)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (4,2) and (x%5B2%5D,y%5B2%5D) is the second point (12,8))


m=%288-2%29%2F%2812-4%29 Plug in y%5B2%5D=8,y%5B1%5D=2,x%5B2%5D=12,x%5B1%5D=4 (these are the coordinates of given points)


m=+6%2F8 Subtract the terms in the numerator 8-2 to get 6. Subtract the terms in the denominator 12-4 to get 8




m=3%2F4 Reduce



So the slope is

m=3%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 (x%5B1%5D,y%5B1%5D) is one of the given points


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


y-2=%283%2F4%29%28x-4%29 Plug in m=3%2F4, x%5B1%5D=4, and y%5B1%5D=2 (these values are given)



y-2=%283%2F4%29x%2B%283%2F4%29%28-4%29 Distribute 3%2F4


y-2=%283%2F4%29x-3 Multiply 3%2F4 and -4 to get -12%2F4. Now reduce -12%2F4 to get -3

y=%283%2F4%29x-3%2B2 Add 2 to both sides to isolate y


y=%283%2F4%29x-1 Combine like terms -3 and 2 to get -1

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Answer:



So the equation of the line which goes through the points (4,2) and (12,8) is:y=%283%2F4%29x-1


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3%2F4 and the y-intercept is b=-1


Notice if we graph the equation y=%283%2F4%29x-1 and plot the points (4,2) and (12,8), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F4%29x-1 through the points (4,2) and (12,8)


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