SOLUTION: using slope formula and point slope formula, write the equation containing the following 2 points. (4,3)(2,-5) equation:

Algebra ->  Linear-equations -> SOLUTION: using slope formula and point slope formula, write the equation containing the following 2 points. (4,3)(2,-5) equation:      Log On


   

Question 235287: using slope formula and point slope formula, write the equation containing the following 2 points.
(4,3)(2,-5)
equation:
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=2 and y%5B2%5D=-5.


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


m=%28-5-3%29%2F%282-4%29 Plug in y%5B2%5D=-5, y%5B1%5D=3, x%5B2%5D=2, and x%5B1%5D=4


m=%28-8%29%2F%282-4%29 Subtract 3 from -5 to get -8


m=%28-8%29%2F%28-2%29 Subtract 4 from 2 to get -2


m=4 Reduce


So the slope of the line that goes through the points and is m=4


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


y-3=4x%2B4%28-4%29 Distribute


y-3=4x-16 Multiply


y=4x-16%2B3 Add 3 to both sides.


y=4x-13 Combine like terms.



So the equation that goes through the points and is y=4x-13


Notice how the graph of y=4x-13 goes through the points and . So this visually verifies our answer.
Graph of y=4x-13 through the points and