SOLUTION: Find the equation of the line that passes through the following two points: (6, – 3) and (4, 1)

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that passes through the following two points: (6, – 3) and (4, 1)       Log On


   

Question 207628: Find the equation of the line that passes through the following two points:
(6, – 3) and (4, 1)

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=6 and y%5B1%5D=-3.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=1.


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


m=%281--3%29%2F%284-6%29 Plug in y%5B2%5D=1, y%5B1%5D=-3, x%5B2%5D=4, and x%5B1%5D=6


m=%284%29%2F%284-6%29 Subtract -3 from 1 to get 4


m=%284%29%2F%28-2%29 Subtract 6 from 4 to get -2


m=-2 Reduce


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


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=-2%28x-6%29 Plug in m=-2, x%5B1%5D=6, and y%5B1%5D=-3


y%2B3=-2%28x-6%29 Rewrite y--3 as y%2B3


y%2B3=-2x%2B-2%28-6%29 Distribute


y%2B3=-2x%2B12 Multiply


y=-2x%2B12-3 Subtract 3 from both sides.


y=-2x%2B9 Combine like terms.


So the equation that goes through the points and is y=-2x%2B9


Notice how the graph of y=-2x%2B9 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B9 through the points and