SOLUTION: What is the equation of a line in slope intercept form that has the endpoints of (3,6)and (7,-2)?

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Question 620573: What is the equation of a line in slope intercept form that has the endpoints of (3,6)and (7,-2)?
Found 2 solutions by jim_thompson5910, lwsshak3:
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=3 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=-2.


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


m=%28-2-6%29%2F%287-3%29 Plug in y%5B2%5D=-2, y%5B1%5D=6, x%5B2%5D=7, and x%5B1%5D=3


m=%28-8%29%2F%287-3%29 Subtract 6 from -2 to get -8


m=%28-8%29%2F%284%29 Subtract 3 from 7 to get 4


m=-2 Reduce


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


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-6=-2%28x-3%29 Plug in m=-2, x%5B1%5D=3, and y%5B1%5D=6


y-6=-2x%2B-2%28-3%29 Distribute


y-6=-2x%2B6 Multiply


y=-2x%2B6%2B6 Add 6 to both sides.


y=-2x%2B12 Combine like terms.


So the equation that goes through the points and is y=-2x%2B12

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What is the equation of a line in slope intercept form that has the endpoints of (3,6)and (7,-2)?
**
Standard form of equation for a straight line: y=mx+b, m=slope, b=y-intercept
For given problem:
slope of line=∆y/∆x=rise/run=(-2-6)/(7-3)=-8/4=-2
equation: y=-2x+b
solve for b using coordinates of either of given points, like (3,6)
6=-2*3+b
b=12
equation of line: y=-2x+12