SOLUTION: Find the slope-intercept form of the line through the points A (2, 2) and B ( - 7, 8).

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the slope-intercept form of the line through the points A (2, 2) and B ( - 7, 8).       Log On


   

Question 353665: Find the slope-intercept form of the line through the points A (2, 2) and B ( - 7, 8).

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


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


m=%288-2%29%2F%28-7-2%29 Plug in y%5B2%5D=8, y%5B1%5D=2, x%5B2%5D=-7, and x%5B1%5D=2


m=%286%29%2F%28-7-2%29 Subtract 2 from 8 to get 6


m=%286%29%2F%28-9%29 Subtract 2 from -7 to get -9


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


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


y-2=%28-2%2F3%29x%2B4%2F3 Multiply


y=%28-2%2F3%29x%2B4%2F3%2B2 Add 2 to both sides.


y=%28-2%2F3%29x%2B10%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=%28-2%2F3%29x%2B10%2F3