SOLUTION: Write the equation of the line passing through (2, –1) and (3, –1).

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Question 101152: Write the equation of the line passing through (2, –1) and (3, –1).
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,-1) and (3,-1)

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,-1) and is the second point (3,-1))

m=%28-1--1%29%2F%283-2%29 Plug in y%5B2%5D=-1,y%5B1%5D=-1,x%5B2%5D=3,x%5B1%5D=2 (these are the coordinates of given points)

m=+0%2F1 Subtract the terms in the numerator -1--1 to get 0. Subtract the terms in the denominator 3-2 to get 1


m=0 Reduce

So the slope is
m=0

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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--1=%280%29%28x-2%29 Plug in m=0, x%5B1%5D=2, and y%5B1%5D=-1 (these values are given)


y%2B1=%280%29%28x-2%29 Rewrite y--1 as y%2B1


y%2B1=0x%2B%280%29%28-2%29 Distribute 0

y%2B1=0x%2B0 Multiply 0 and -2 to get 0%2F0. Now reduce 0%2F0 to get 0

y=0x%2B0-1 Subtract 1 from both sides to isolate y

y=0x-1 Combine like terms 0 and -1 to get -1

y=-1 Remove the zero term
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Answer:


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

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=0 and the y-intercept is b=-1

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

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

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