SOLUTION: Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant. where the coordinates are (2,2) and (-2,-2)

Algebra ->  Graphs -> SOLUTION: Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant. where the coordinates are (2,2) and (-2,-2)      Log On


   

Question 472336: Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant. where the coordinates are (2,2) and (-2,-2)
Found 2 solutions by MathLover1, richard1234:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
the coordinates are (2,2) and (-2,-2)...find a line that passes through these points

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-2,-2) and (2,2)


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


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


m=+4%2F4 Subtract the terms in the numerator 2--2 to get 4. Subtract the terms in the denominator 2--2 to get 4




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



y%2B2=%281%29%28x--2%29 Rewrite y--2 as y%2B2



y%2B2=%281%29%28x%2B2%29 Rewrite x--2 as x%2B2



y%2B2=1x%2B%281%29%282%29 Distribute 1


y%2B2=1x%2B2 Multiply 1 and 2 to get 2%2F1. Now reduce 2%2F1 to get 2

y=1x%2B2-2 Subtract 2 from both sides to isolate y


y=1x%2B0 Combine like terms 2 and -2 to get 0

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Answer:



So the equation of the line which goes through the points (-2,-2) and (2,2) is:y=1x%2B0


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=0


Notice if we graph the equation y=1x%2B0 and plot the points (-2,-2) and (2,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1x%2B0 through the points (-2,-2) and (2,2)


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




note: the constant b=0

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
For both points, the x-coordinate maps to itself, so intuitively, we would say y = x is the only solution.

Or, we could set up a system of equations, e.g.

2 = 2m + b
-2 = -2m + b

Adding both equations produces 2b = 0 --> b = 0. From this we get m = 1.