SOLUTION: Find an equation for the line with the given properties,express the equation in slope-intercept form. P=(-3,-5) and Q=(-2,-3) What is equation line?

Algebra ->  College  -> Linear Algebra -> SOLUTION: Find an equation for the line with the given properties,express the equation in slope-intercept form. P=(-3,-5) and Q=(-2,-3) What is equation line?      Log On


   

Question 626708: Find an equation for the line with the given properties,express the equation in slope-intercept form.
P=(-3,-5) and Q=(-2,-3)
What is equation line?
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=-3 and y%5B1%5D=-5.
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=%28-3--5%29%2F%28-2--3%29 Plug in y%5B2%5D=-3, y%5B1%5D=-5, x%5B2%5D=-2, and x%5B1%5D=-3


m=%282%29%2F%28-2--3%29 Subtract -5 from -3 to get 2


m=%282%29%2F%281%29 Subtract -3 from -2 to get 1


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


y--5=2%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B5=2%28x%2B3%29 Rewrite y--5 as y%2B5


y%2B5=2x%2B2%283%29 Distribute


y%2B5=2x%2B6 Multiply


y=2x%2B6-5 Subtract 5 from both sides.


y=2x%2B1 Combine like terms.


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


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