SOLUTION: Write the equation of the line through points (-2,3) and (4,8)

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Question 101296: Write the equation of the line through points (-2,3) and (4,8)
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 (-2,3) and (4,8)

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 (-2,3) and is the second point (4,8))

m=%288-3%29%2F%284--2%29 Plug in y%5B2%5D=8,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-2 (these are the coordinates of given points)

m=+5%2F6 Subtract the terms in the numerator 8-3 to get 5. Subtract the terms in the denominator 4--2 to get 6

So the slope is
m=5%2F6

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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=%285%2F6%29%28x--2%29 Plug in m=5%2F6, x%5B1%5D=-2, and y%5B1%5D=3 (these values are given)


y-3=%285%2F6%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=%285%2F6%29x%2B%285%2F6%29%282%29 Distribute 5%2F6

y-3=%285%2F6%29x%2B5%2F3 Multiply 5%2F6 and 2 to get 10%2F6. Now reduce 10%2F6 to get 5%2F3

y=%285%2F6%29x%2B5%2F3%2B3 Add 3 to both sides to isolate y

y=%285%2F6%29x%2B14%2F3 Combine like terms 5%2F3 and 3 to get 14%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 (-2,3) and (4,8) is:y=%285%2F6%29x%2B14%2F3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=5%2F6 and the y-intercept is b=14%2F3

Notice if we graph the equation y=%285%2F6%29x%2B14%2F3 and plot the points (-2,3) and (4,8), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%285%2F6%29x%2B14%2F3 through the points (-2,3) and (4,8)

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