SOLUTION: What’s the equation of a line that passes through points (0, -1) and (2, 3)? Please help me with step by step on this. Thank you

Algebra ->  Linear-equations -> SOLUTION: What’s the equation of a line that passes through points (0, -1) and (2, 3)? Please help me with step by step on this. Thank you      Log On


   

Question 887716: What’s the equation of a line that passes through points (0, -1) and (2, 3)?
Please help me with step by step on this.
Thank you
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=0 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=2 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--1%29%2F%282-0%29 Plug in y%5B2%5D=3, y%5B1%5D=-1, x%5B2%5D=2, and x%5B1%5D=0


m=%284%29%2F%282-0%29 Subtract -1 from 3 to get 4


m=%284%29%2F%282%29 Subtract 0 from 2 to get 2


m=2 Reduce


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


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--1=2%28x-0%29 Plug in m=2, x%5B1%5D=0, and y%5B1%5D=-1


y%2B1=2%28x-0%29 Rewrite y--1 as y%2B1


y%2B1=2x%2B2%28-0%29 Distribute


y%2B1=2x%2B0 Multiply


y=2x%2B0-1 Subtract 1 from both sides.


y=2x-1 Combine like terms.


So the equation that goes through the points and is y=2x-1


Notice how the graph of y=2x-1 goes through the points and . So this visually verifies our answer.
Graph of y=2x-1 through the points and