SOLUTION: Please help me solve this equation:found the equation of the line that passes through the pair of points (-1,1),(-4,2)

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Question 130002: Please help me solve this equation:found the equation of the line that passes through the pair of points (-1,1),(-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 (-1,1) 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 (-1,1) and is the second point (-4,2))

m=%282-1%29%2F%28-4--1%29 Plug in y%5B2%5D=2,y%5B1%5D=1,x%5B2%5D=-4,x%5B1%5D=-1 (these are the coordinates of given points)

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


m=-1%2F3 Reduce

So the slope is
m=-1%2F3

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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%2F3%29%28x--1%29 Plug in m=-1%2F3, x%5B1%5D=-1, and y%5B1%5D=1 (these values are given)


y-1=%28-1%2F3%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-1=%28-1%2F3%29x%2B%28-1%2F3%29%281%29 Distribute -1%2F3

y-1=%28-1%2F3%29x-1%2F3 Multiply -1%2F3 and 1 to get -1%2F3

y=%28-1%2F3%29x-1%2F3%2B1 Add 1 to both sides to isolate y

y=%28-1%2F3%29x%2B2%2F3 Combine like terms -1%2F3 and 1 to get 2%2F3 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line which goes through the points (-1,1) and (-4,2) is:y=%28-1%2F3%29x%2B2%2F3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F3 and the y-intercept is b=2%2F3

Notice if we graph the equation y=%28-1%2F3%29x%2B2%2F3 and plot the points (-1,1) and (-4,2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x%2B2%2F3 through the points (-1,1) and (-4,2)

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