SOLUTION: Write an equation of the line that passes through the points (-5,3) and (5,-3).

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Question 200776: Write an equation of the line that passes through the points (-5,3) and (5,-3).
Found 2 solutions by jim_thompson5910, checkley77:
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 and is the second point .


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


m=%28-3-3%29%2F%285--5%29 Plug in y%5B2%5D=-3, y%5B1%5D=3, x%5B2%5D=5, and x%5B1%5D=-5


m=%28-6%29%2F%285--5%29 Subtract 3 from -3 to get -6


m=%28-6%29%2F%2810%29 Subtract -5 from 5 to get 10


m=-3%2F5 Reduce


So the slope of the line that goes through the points and is m=-3%2F5


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=%28-3%2F5%29%28x--5%29 Plug in m=-3%2F5, x%5B1%5D=-5, and y%5B1%5D=3


y-3=%28-3%2F5%29%28x%2B5%29 Rewrite x--5 as x%2B5


y-3=%28-3%2F5%29x%2B%28-3%2F5%29%285%29 Distribute


y-3=%28-3%2F5%29x-3 Multiply


y=%28-3%2F5%29x-3%2B3 Add 3 to both sides.


y=%28-3%2F5%29x%2B0 Combine like terms.


y=%28-3%2F5%29x Remove the trailing zero


y=%28-3%2F5%29x Simplify


So the equation that goes through the points and is y=%28-3%2F5%29x


Notice how the graph of y=%28-3%2F5%29x goes through the points and . So this visually verifies our answer.
Graph of y=%28-3%2F5%29x through the points and

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(-5,3) and (5,-3)
First we need to find the slope (m) in the line equation Y=mX+b.
m=(y2-y1)/(x2-x1)
m=(-3-3)/(5+5)=-6/10 is the slope.
Now replacing the X+Y terms with one set of X & Y values we solve for the Y intercept (b).
3=-6/10*-5+b
3=30/10+b
b=3-30/10
b=3-3
b=0 which is the Y intercept.
Y=-6x/10 is the line equation which runs through the points (-5,3) & (5,-3).
Proof:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+-6x%2F10+%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -6x/10).