SOLUTION: write an equation of the line passing through (-3,8) (5,4)

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Question 101532: write an equation of the line passing through (-3,8) (5,4)
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 (-3,8) and (5,4)


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 (-3,8) and (x%5B2%5D,y%5B2%5D) is the second point (5,4))


m=%284-8%29%2F%285--3%29 Plug in y%5B2%5D=4,y%5B1%5D=8,x%5B2%5D=5,x%5B1%5D=-3 (these are the coordinates of given points)


m=+-4%2F8 Subtract the terms in the numerator 4-8 to get -4. Subtract the terms in the denominator 5--3 to get 8




m=-1%2F2 Reduce



So the slope is

m=-1%2F2





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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-8=%28-1%2F2%29%28x--3%29 Plug in m=-1%2F2, x%5B1%5D=-3, and y%5B1%5D=8 (these values are given)



y-8=%28-1%2F2%29%28x%2B3%29 Rewrite x--3 as x%2B3



y-8=%28-1%2F2%29x%2B%28-1%2F2%29%283%29 Distribute -1%2F2


y-8=%28-1%2F2%29x-3%2F2 Multiply -1%2F2 and 3 to get -3%2F2

y=%28-1%2F2%29x-3%2F2%2B8 Add 8 to both sides to isolate y


y=%28-1%2F2%29x%2B13%2F2 Combine like terms -3%2F2 and 8 to get 13%2F2 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (-3,8) and (5,4) is:y=%28-1%2F2%29x%2B13%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=13%2F2


Notice if we graph the equation y=%28-1%2F2%29x%2B13%2F2 and plot the points (-3,8) and (5,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B13%2F2 through the points (-3,8) and (5,4)


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