SOLUTION: Find the equation of the line that passes through the points (2,-3) and (-1,-2)

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Question 119134: Find the equation of the line that passes through the points (2,-3) and (-1,-2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (2,-3) and (-1,-2)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (2,-3) and is the second point (-1,-2))

m=%28-2--3%29%2F%28-1-2%29 Plug in y%5B2%5D=-2,y%5B1%5D=-3,x%5B2%5D=-1,x%5B1%5D=2 (these are the coordinates of given points)

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


m=-1%2F3 Reduce

So the slope is
m=-1%2F3

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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 is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y--3=%28-1%2F3%29%28x-2%29 Plug in m=-1%2F3, x%5B1%5D=2, and y%5B1%5D=-3 (these values are given)


y%2B3=%28-1%2F3%29%28x-2%29 Rewrite y--3 as y%2B3


y%2B3=%28-1%2F3%29x%2B%28-1%2F3%29%28-2%29 Distribute -1%2F3

y%2B3=%28-1%2F3%29x%2B2%2F3 Multiply -1%2F3 and -2 to get 2%2F3

y=%28-1%2F3%29x%2B2%2F3-3 Subtract 3 from both sides to isolate y

y=%28-1%2F3%29x-7%2F3 Combine like terms 2%2F3 and -3 to get -7%2F3 (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 (2,-3) and (-1,-2) is:y=%28-1%2F3%29x-7%2F3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F3 and the y-intercept is b=-7%2F3

Notice if we graph the equation y=%28-1%2F3%29x-7%2F3 and plot the points (2,-3) and (-1,-2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x-7%2F3 through the points (2,-3) and (-1,-2)

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