SOLUTION: Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)? A step-by-step solved answer would be very helpful, as well as side notes as to wha

Algebra ->  Linear-equations -> SOLUTION: Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)? A step-by-step solved answer would be very helpful, as well as side notes as to wha      Log On


   

Question 526995: Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)?

A step-by-step solved answer would be very helpful, as well as side notes as to what is happening in each step. Thank you!
-Laura DiPietro
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=-1.
Also, is the second point . So this means that x%5B2%5D=-4 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=%28-3--1%29%2F%28-4--2%29 Plug in y%5B2%5D=-3, y%5B1%5D=-1, x%5B2%5D=-4, and x%5B1%5D=-2


m=%28-2%29%2F%28-4--2%29 Subtract -1 from -3 to get -2


m=%28-2%29%2F%28-2%29 Subtract -2 from -4 to get -2


m=1 Reduce


So the slope of the line that goes through the points and is m=1


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


y--1=1%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B1=1%28x%2B2%29 Rewrite y--1 as y%2B1


y%2B1=1x%2B1%282%29 Distribute


y%2B1=1x%2B2 Multiply


y=1x%2B2-1 Subtract 1 from both sides.


y=1x%2B1 Combine like terms.


y=x%2B1 Simplify


So the equation that goes through the points and is y=x%2B1



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Jim