SOLUTION: The coordinates of points A and B are (2,1) and (1,2). what is the slope of line AB? what is an equation of line AB?

Algebra ->  Linear-equations -> SOLUTION: The coordinates of points A and B are (2,1) and (1,2). what is the slope of line AB? what is an equation of line AB?      Log On


   

Question 117384: The coordinates of points A and B are (2,1) and (1,2).
what is the slope of line AB?
what is an equation of line AB?
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 (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 (2,1) and is the second point (1,2))

m=%282-1%29%2F%281-2%29 Plug in y%5B2%5D=2,y%5B1%5D=1,x%5B2%5D=1,x%5B1%5D=2 (these are the coordinates of given points)

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


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 is one of the given points

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

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


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

y-1=-x%2B2 Multiply -1 and -2 to get 2

y=-x%2B2%2B1 Add 1 to both sides to isolate y

y=-x%2B3 Combine like terms 2 and 1 to get 3
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Answer:


So the equation of the line which goes through the points (2,1) and (1,2) is:y=-x%2B3

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=3

Notice if we graph the equation y=-x%2B3 and plot the points (2,1) and (1,2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B3 through the points (2,1) and (1,2)

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