SOLUTION: find the equation of the line (in the slope-intercept form)that goes through the points (8,3) and (5,-7)

Algebra ->  Graphs -> SOLUTION: find the equation of the line (in the slope-intercept form)that goes through the points (8,3) and (5,-7)      Log On


   

Question 512031: find the equation of the line (in the slope-intercept form)that goes through the points (8,3) and (5,-7)
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=5 and y%5B2%5D=-7.


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


m=%28-7-3%29%2F%285-8%29 Plug in y%5B2%5D=-7, y%5B1%5D=3, x%5B2%5D=5, and x%5B1%5D=8


m=%28-10%29%2F%285-8%29 Subtract 3 from -7 to get -10


m=%28-10%29%2F%28-3%29 Subtract 8 from 5 to get -3


m=10%2F3 Reduce


So the slope of the line that goes through the points and is m=10%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=%2810%2F3%29%28x-8%29 Plug in m=10%2F3, x%5B1%5D=8, and y%5B1%5D=3


y-3=%2810%2F3%29x%2B%2810%2F3%29%28-8%29 Distribute


y-3=%2810%2F3%29x-80%2F3 Multiply


y=%2810%2F3%29x-80%2F3%2B3 Add 3 to both sides.


y=%2810%2F3%29x-71%2F3 Combine like terms.


So the answer is y=%2810%2F3%29x-71%2F3