SOLUTION: Choose the equation of the line that contains the points (-3, 2) and (5, -5).

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Question 1044818: Choose the equation of the line that contains the points (-3, 2) and (5, -5).
Answer by MathLover1(20849) 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 (-3,2) and (5,-5)


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 (-3,2) and (x%5B2%5D,y%5B2%5D) is the second point (5,-5))


m=%28-5-2%29%2F%285--3%29 Plug in y%5B2%5D=-5,y%5B1%5D=2,x%5B2%5D=5,x%5B1%5D=-3 (these are the coordinates of given points)


m=+-7%2F8 Subtract the terms in the numerator -5-2 to get -7. Subtract the terms in the denominator 5--3 to get 8



So the slope is

m=-7%2F8





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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=%28-7%2F8%29%28x--3%29 Plug in m=-7%2F8, x%5B1%5D=-3, and y%5B1%5D=2 (these values are given)



y-2=%28-7%2F8%29%28x%2B3%29 Rewrite x--3 as x%2B3



y-2=%28-7%2F8%29x%2B%28-7%2F8%29%283%29 Distribute -7%2F8


y-2=%28-7%2F8%29x-21%2F8 Multiply -7%2F8 and 3 to get -21%2F8

y=%28-7%2F8%29x-21%2F8%2B2 Add 2 to both sides to isolate y


y=%28-7%2F8%29x-5%2F8 Combine like terms -21%2F8 and 2 to get -5%2F8 (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 (-3,2) and (5,-5) is:y=%28-7%2F8%29x-5%2F8


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-7%2F8 and the y-intercept is b=-5%2F8


Notice if we graph the equation y=%28-7%2F8%29x-5%2F8 and plot the points (-3,2) and (5,-5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-7%2F8%29x-5%2F8 through the points (-3,2) and (5,-5)


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