SOLUTION: Write the slope-intercept equation for the line containing the given pair of points. (-6,-2) and (3,4)

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept equation for the line containing the given pair of points. (-6,-2) and (3,4)      Log On


   

Question 745226: Write the slope-intercept equation for the line containing the given pair of points.
(-6,-2) and (3,4)
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=-6 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=4.


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


m=%284--2%29%2F%283--6%29 Plug in y%5B2%5D=4, y%5B1%5D=-2, x%5B2%5D=3, and x%5B1%5D=-6


m=%286%29%2F%283--6%29 Subtract -2 from 4 to get 6


m=%286%29%2F%289%29 Subtract -6 from 3 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=%282%2F3%29%28x--6%29 Plug in m=2%2F3, x%5B1%5D=-6, and y%5B1%5D=-2


y--2=%282%2F3%29%28x%2B6%29 Rewrite x--6 as x%2B6


y%2B2=%282%2F3%29%28x%2B6%29 Rewrite y--2 as y%2B2


y%2B2=%282%2F3%29x%2B%282%2F3%29%286%29 Distribute


y%2B2=%282%2F3%29x%2B4 Multiply


y=%282%2F3%29x%2B4-2 Subtract 2 from both sides.


y=%282%2F3%29x%2B2 Combine like terms.


So the equation that goes through the points and is y=%282%2F3%29x%2B2