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

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


   

Question 117670: Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible.
Problem: (-1, 3) and (4, -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 (-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: is the first point (-1,3) and 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 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

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.