SOLUTION: What is the equation of the line in slope-intercept form passing through (-5,2) and (2,9)?

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Question 82872: What is the equation of the line in slope-intercept form passing through (-5,2) and (2,9)?
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 (-5,2) and (2,9)


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 (-5,2) and (x%5B2%5D,y%5B2%5D) is the second point (2,9))


m=%289-2%29%2F%282--5%29 Plug in y%5B2%5D=9,y%5B1%5D=2,x%5B2%5D=2,x%5B1%5D=-5 (these are the coordinates of given points)


m=+7%2F7 Subtract the terms in the numerator 9-2 to get 7. Subtract the terms in the denominator 2--5 to get 7




m=1 Reduce



So the slope is

m=1





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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=%281%29%28x--5%29 Plug in m=1, x%5B1%5D=-5, and y%5B1%5D=2 (these values are given)



y-2=%281%29%28x%2B5%29 Rewrite x--5 as x%2B5



y-2=1x%2B%281%29%285%29 Distribute 1


y-2=1x%2B5 Multiply 1 and 5 to get 5%2F1. Now reduce 5%2F1 to get 5

y=1x%2B5%2B2 Add 2 to both sides to isolate y


y=1x%2B7 Combine like terms 5 and 2 to get 7

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Answer:



So the equation of the line which goes through the points (-5,2) and (2,9) is:y=1x%2B7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1 and the y-intercept is b=7


Notice if we graph the equation y=1x%2B7 and plot the points (-5,2) and (2,9), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1x%2B7 through the points (-5,2) and (2,9)


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