SOLUTION: find an equation in Slope-Intercept Form of the line that goes through (8,3) and (2,-1)

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Question 778130: find an equation in Slope-Intercept Form of the line that goes through (8,3) and (2,-1)
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=8 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=-1.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-1-3%29%2F%282-8%29 Plug in y%5B2%5D=-1, y%5B1%5D=3, x%5B2%5D=2, and x%5B1%5D=8


m=%28-4%29%2F%282-8%29 Subtract 3 from -1 to get -4


m=%28-4%29%2F%28-6%29 Subtract 8 from 2 to get -6


m=2%2F3 Reduce


So the slope of the line that goes through the points and is m=2%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-3=%282%2F3%29%28x-8%29 Plug in m=2%2F3, x%5B1%5D=8, and y%5B1%5D=3


y-3=%282%2F3%29x%2B%282%2F3%29%28-8%29 Distribute


y-3=%282%2F3%29x-16%2F3 Multiply


y=%282%2F3%29x-16%2F3%2B3 Add 3 to both sides.


y=%282%2F3%29x-7%2F3 Combine like terms. note: If you need help with fractions, check out this solver.



So the equation that goes through the points and is y=%282%2F3%29x-7%2F3

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Find the equation of line going through points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (8, 3) and (x2, y2) = (2, -1).
Slope a is .
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 0.666666666666667%2A8+%2Bb+=+-2.33333333333333. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=3-0.666666666666667%2A8+=+-2.33333333333333.

y=(0.666666666666667)x + (-2.33333333333333)

Your graph: