SOLUTION: passes through points (-2,-3) and (3,3)

Algebra ->  Graphs -> SOLUTION: passes through points (-2,-3) and (3,3)       Log On


   

Question 293190: passes through points (-2,-3) and (3,3)
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Is this a guessing game?
Should we guess what passes through those points?
a circle? a line ? a parabola? a square?

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


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


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


m=%286%29%2F%283--2%29 Subtract -3 from 3 to get 6


m=%286%29%2F%285%29 Subtract -2 from 3 to get 5


So the slope of the line that goes through the points and is m=6%2F5


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=%286%2F5%29%28x--2%29 Plug in m=6%2F5, x%5B1%5D=-2, and y%5B1%5D=-3


y--3=%286%2F5%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B3=%286%2F5%29%28x%2B2%29 Rewrite y--3 as y%2B3


y%2B3=%286%2F5%29x%2B%286%2F5%29%282%29 Distribute


y%2B3=%286%2F5%29x%2B12%2F5 Multiply


y=%286%2F5%29x%2B12%2F5-3 Subtract 3 from both sides.


y=%286%2F5%29x-3%2F5 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=%286%2F5%29x-3%2F5