SOLUTION: Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form. #1: (-1, 3) and (4, -2) #2: (2, -3) and (2, 4)

Algebra ->  Coordinate-system -> SOLUTION: Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form. #1: (-1, 3) and (4, -2) #2: (2, -3) and (2, 4)       Log On


   

Question 87255: Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form.
#1: (-1, 3) and (4, -2)
#2: (2, -3) and (2, 4)
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,3) and (4,-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 (-1,3) and (x%5B2%5D,y%5B2%5D) is the second point (4,-2))


m=%28-2-3%29%2F%284--1%29 Plug in y%5B2%5D=-2,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-1 (these are the coordinates of given points)


m=+-5%2F5 Subtract the terms in the numerator -2-3 to get -5. Subtract the terms in the denominator 4--1 to get 5




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



y-3=%28-1%29%28x%2B1%29 Rewrite x--1 as x%2B1



y-3=-x%2B%28-1%29%281%29 Distribute -1


y-3=-x-1 Multiply -1 and 1 to get -1%2F1. Now reduce -1%2F1 to get -1

y=-x-1%2B3 Add 3 to both sides to isolate y


y=-x%2B2 Combine like terms -1 and 3 to get 2

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Answer:



So the equation of the line which goes through the points (-1,3) and (4,-2) is:y=-x%2B2


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=2


Notice if we graph the equation y=-x%2B2 and plot the points (-1,3) and (4,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-x%2B2 through the points (-1,3) and (4,-2)


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





#2
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (2,-3) and (2,4)


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 (2,4))


m=%284--3%29%2F%282-2%29 Plug in y%5B2%5D=4,y%5B1%5D=-3,x%5B2%5D=2,x%5B1%5D=2 (these are the coordinates of given points)


m=+7%2F0 Subtract the terms in the numerator 4--3 to get 7. Subtract the terms in the denominator 2-2 to get 0




Since the denominator is zero, the slope is undefined (remember you cannot divide by zero). So we cannot use the slope intercept form to write an equation. So we can only say that the equation is a vertical line through x=2, which means the equation is x=2 (notice this is not in slope-intercept form)



So the equation x=2 looks like this:

Graph of x=2 through the points (2,-3) and (2,4)