SOLUTION: What is the equation of line passing through (2,-3) and (4,-4)? Write the equation in the standard form. (Ax + By + C)

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Question 171387: What is the equation of line passing through (2,-3) and (4,-4)?
Write the equation in the standard form. (Ax + By + C)
Found 2 solutions by jim_thompson5910, 1-10math:
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=%28-4--3%29%2F%284-2%29 Plug in y%5B2%5D=-4, y%5B1%5D=-3, x%5B2%5D=4, and x%5B1%5D=2


m=%28-1%29%2F%284-2%29 Subtract -3 from -4 to get -1


m=%28-1%29%2F%282%29 Subtract 2 from 4 to get 2


So the slope of the line that goes through the points and is m=-1%2F2


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=%28-1%2F2%29%28x-2%29 Plug in m=-1%2F2, x%5B1%5D=2, and y%5B1%5D=-3


y%2B3=%28-1%2F2%29%28x-2%29 Rewrite y--3 as y%2B3


y%2B3=%28-1%2F2%29x%2B%28-1%2F2%29%28-2%29 Distribute


y%2B3=%28-1%2F2%29x%2B1 Multiply


2y%2B6=-x%2B2 Multiply EVERY term by the LCD 2 to clear the fraction.


2y%2B6%2Bx=2 Add "x" to both sides.


2y%2Bx=2-6 Subtract 6 from both sides.


x%2B2y=-4 Combine and rearrange the terms.



So the line that passes through (2,-3) and (4,-4) is x%2B2y=-4

Answer by 1-10math(1) About Me  (Show Source):
You can put this solution on YOUR website!
y+4=-1/3(x-4)
y+4=-1/3x-1(1/3)
y+4+1/3x=-1(1/3)
-4
y+1/3x=-1(1/3)-4