SOLUTION: Write in STANDARD FORM an equation of the line that passes through: (-3,3) and (7,2)

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Question 74215: Write in STANDARD FORM an equation of the line that passes through: (-3,3) and (7,2)
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 (7,2)


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 (7,2))


m=%282-3%29%2F%287--3%29 Plug in y%5B2%5D=2,y%5B1%5D=3,x%5B2%5D=7,x%5B1%5D=-3 (these are the coordinates of given points)


m=+-1%2F10 Subtract the terms in the numerator 2-3 to get -1. Subtract the terms in the denominator 7--3 to get 10



So the slope is

m=-1%2F10





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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=%28-1%2F10%29%28x--3%29 Plug in m=-1%2F10, x%5B1%5D=-3, and y%5B1%5D=3 (these values are given)



y-3=%28-1%2F10%29%28x%2B3%29 Rewrite x--3 as x%2B3



y-3=%28-1%2F10%29x%2B%28-1%2F10%29%283%29 Distribute -1%2F10


y-3=%28-1%2F10%29x-3%2F10 Multiply -1%2F10 and 3 to get -3%2F10

y=%28-1%2F10%29x-3%2F10%2B3 Add 3 to both sides to isolate y


y=%28-1%2F10%29x%2B27%2F10 Combine like terms -3%2F10 and 3 to get 27%2F10 (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 (7,2) is:y=%28-1%2F10%29x%2B27%2F10


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F10 and the y-intercept is b=27%2F10


Notice if we graph the equation y=%28-1%2F10%29x%2B27%2F10 and plot the points (-3,3) and (7,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F10%29x%2B27%2F10 through the points (-3,3) and (7,2)


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



So we know that our slope-intercept equation is
y=%28-1%2F10%29x%2B27%2F10 or y=-0.1x%2B2.7
So we need to get the x's and the y's to one side
y%2B%281%2F10%29x=27%2F10
Now we need to multiply everything by 10 (which is our LCD) to get nothing but integers.
10%28y%2B%281%2Fcross%2810%29%29x%29=cross%2810%29%2827%2Fcross%2810%29%29
So we get
10y%2Bx=27
So our standard equation is:
x%2B10y=27
Where A=1, B=10, and C=27