SOLUTION: 1. Line j contains the points (-2,3) and (1,5). a) Determine the slope of the line.---I got that part. slope=2/3 b) Write an equation for the line. y=2/3x+ ??? I nee

Algebra ->  Graphs -> SOLUTION: 1. Line j contains the points (-2,3) and (1,5). a) Determine the slope of the line.---I got that part. slope=2/3 b) Write an equation for the line. y=2/3x+ ??? I nee      Log On


   

Question 148201: 1. Line j contains the points (-2,3) and (1,5).
a) Determine the slope of the line.---I got that part. slope=2/3
b) Write an equation for the line.
y=2/3x+ ???
I need help right there.
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=%285-3%29%2F%281--2%29 Plug in y%5B2%5D=5, y%5B1%5D=3, x%5B2%5D=1, x%5B1%5D=-2, ,


m=%282%29%2F%281--2%29 Subtract 3 from 5 to get 2


m=%282%29%2F%283%29 Subtract -2 from 1 to get 3


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-3=%282%2F3%29%28x--2%29 Plug in m=2%2F3, x%5B1%5D=-2, and y%5B1%5D=3


y-3=%282%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=%282%2F3%29x%2B%282%2F3%29%282%29 Distribute


y-3=%282%2F3%29x%2B4%2F3 Multiply


y=%282%2F3%29x%2B4%2F3%2B3 Add 3 to both sides.


y=%282%2F3%29x%2B4%2F3%2B9%2F3 Rewrite 3 as 9%2F3.


y=%282%2F3%29x%2B13%2F3 Combine the fractions.



So the equation that goes through the points and is y=%282%2F3%29x%2B13%2F3


Notice how the graph of y=%282%2F3%29x%2B13%2F3 goes through the points and . So this visually verifies our answer.
Graph of y=%282%2F3%29x%2B13%2F3 through the points and