SOLUTION: Write the slope-intercept equation for the line that passes through (-4, -3) and (-6, 7).

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept equation for the line that passes through (-4, -3) and (-6, 7).       Log On


   

Question 530095: Write the slope-intercept equation for the line that passes through (-4, -3) and (-6, 7).
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=-4 and y%5B1%5D=-3.
Also, is the second point . So this means that x%5B2%5D=-6 and y%5B2%5D=7.


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


m=%287--3%29%2F%28-6--4%29 Plug in y%5B2%5D=7, y%5B1%5D=-3, x%5B2%5D=-6, and x%5B1%5D=-4


m=%2810%29%2F%28-6--4%29 Subtract -3 from 7 to get 10


m=%2810%29%2F%28-2%29 Subtract -4 from -6 to get -2


m=-5 Reduce


So the slope of the line that goes through the points and is m=-5


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=-5%28x--4%29 Plug in m=-5, x%5B1%5D=-4, and y%5B1%5D=-3


y--3=-5%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B3=-5%28x%2B4%29 Rewrite y--3 as y%2B3


y%2B3=-5x%2B-5%284%29 Distribute


y%2B3=-5x-20 Multiply


y=-5x-20-3 Subtract 3 from both sides.


y=-5x-23 Combine like terms.


So the equation that goes through the points and is y=-5x-23


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