SOLUTION: Please help Write the equation of the line passing through each of the given pairs of points. (-3, 3) and (4, -2) Write your results in slope-intercept form, where possible.

Algebra ->  Linear-equations -> SOLUTION: Please help Write the equation of the line passing through each of the given pairs of points. (-3, 3) and (4, -2) Write your results in slope-intercept form, where possible.      Log On


   

Question 111575: Please help
Write the equation of the line passing through each of the given pairs of points.
(-3, 3) and (4, -2)
Write your results in slope-intercept form, where possible.
Thanks
JMS
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 (-3,3) and (4,-2)


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 (-3,3) and (x%5B2%5D,y%5B2%5D) is the second point (4,-2))


m=%28-2-3%29%2F%284--3%29 Plug in y%5B2%5D=-2,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-3 (these are the coordinates of given points)


m=+-5%2F7 Subtract the terms in the numerator -2-3 to get -5. Subtract the terms in the denominator 4--3 to get 7



So the slope is

m=-5%2F7





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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-3=%28-5%2F7%29%28x--3%29 Plug in m=-5%2F7, x%5B1%5D=-3, and y%5B1%5D=3 (these values are given)



y-3=%28-5%2F7%29%28x%2B3%29 Rewrite x--3 as x%2B3



y-3=%28-5%2F7%29x%2B%28-5%2F7%29%283%29 Distribute -5%2F7


y-3=%28-5%2F7%29x-15%2F7 Multiply -5%2F7 and 3 to get -15%2F7

y=%28-5%2F7%29x-15%2F7%2B3 Add 3 to both sides to isolate y


y=%28-5%2F7%29x%2B6%2F7 Combine like terms -15%2F7 and 3 to get 6%2F7 (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 (-3,3) and (4,-2) is:y=%28-5%2F7%29x%2B6%2F7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F7 and the y-intercept is b=6%2F7


Notice if we graph the equation y=%28-5%2F7%29x%2B6%2F7 and plot the points (-3,3) and (4,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-5%2F7%29x%2B6%2F7 through the points (-3,3) and (4,-2)


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