SOLUTION: Find the slope of the line passing through the points (0, -4) and (-6, 7).

Algebra ->  Rational-functions -> SOLUTION: Find the slope of the line passing through the points (0, -4) and (-6, 7).       Log On


   

Question 255379: Find the slope of the line passing through the points (0, -4) 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=0 and y%5B1%5D=-4.
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--4%29%2F%28-6-0%29 Plug in y%5B2%5D=7, y%5B1%5D=-4, x%5B2%5D=-6, and x%5B1%5D=0


m=%2811%29%2F%28-6-0%29 Subtract -4 from 7 to get 11


m=%2811%29%2F%28-6%29 Subtract 0 from -6 to get -6


m=-11%2F6 Reduce


So the slope of the line that goes through the points and is m=-11%2F6


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--4=%28-11%2F6%29%28x-0%29 Plug in m=-11%2F6, x%5B1%5D=0, and y%5B1%5D=-4


y%2B4=%28-11%2F6%29%28x-0%29 Rewrite y--4 as y%2B4


y%2B4=%28-11%2F6%29x%2B%28-11%2F6%29%280%29 Distribute


y%2B4=%28-11%2F6%29x%2B0 Multiply


y=%28-11%2F6%29x%2B0-4 Subtract 4 from both sides.


y=%28-11%2F6%29x-4 Combine like terms.


So the equation that goes through the points and is y=%28-11%2F6%29x-4


Notice how the graph of y=%28-11%2F6%29x-4 goes through the points and . So this visually verifies our answer.


Graph of y=%28-11%2F6%29x-4 through the points and