SOLUTION: Write the equation of the line passing through (2,3) and (-3,-7) in slope-intercept form? By the way, thank you for your continued help, much appreciated! karen

Algebra ->  Functions -> SOLUTION: Write the equation of the line passing through (2,3) and (-3,-7) in slope-intercept form? By the way, thank you for your continued help, much appreciated! karen      Log On


   

Question 181820: Write the equation of the line passing through (2,3) and (-3,-7) in slope-intercept form?
By the way, thank you for your continued help, much appreciated!
karen
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 (2,3) and (-3,-7)


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 (2,3) and (x%5B2%5D,y%5B2%5D) is the second point (-3,-7))


m=%28-7-3%29%2F%28-3-2%29 Plug in y%5B2%5D=-7,y%5B1%5D=3,x%5B2%5D=-3,x%5B1%5D=2 (these are the coordinates of given points)


m=+-10%2F-5 Subtract the terms in the numerator -7-3 to get -10. Subtract the terms in the denominator -3-2 to get -5




m=2 Reduce



So the slope is

m=2





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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=%282%29%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=3 (these values are given)



y-3=2x%2B%282%29%28-2%29 Distribute 2


y-3=2x-4 Multiply 2 and -2 to get -4%2F1. Now reduce -4%2F1 to get -4

y=2x-4%2B3 Add 3 to both sides to isolate y


y=2x-1 Combine like terms -4 and 3 to get -1

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Answer:



So the equation of the line which goes through the points (2,3) and (-3,-7) is:y=2x-1


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


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


Graph of y=2x-1 through the points (2,3) and (-3,-7)


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