SOLUTION: Write the slope-intercept equation for the line that passes through (2, -7) and (4, -13). Please show all of your work

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept equation for the line that passes through (2, -7) and (4, -13). Please show all of your work      Log On


   

Question 385761: Write the slope-intercept equation for the line that passes through (2, -7) and (4, -13). Please show all of your work
Found 2 solutions by rfer, jim_thompson5910:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
m=-6/2
m=-3
-----------------
y=mx+b
-7=-3*2+b
-7=-6+b
b=-1
----------------
y=-3x-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=2 and y%5B1%5D=-7.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=-13.


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


m=%28-13--7%29%2F%284-2%29 Plug in y%5B2%5D=-13, y%5B1%5D=-7, x%5B2%5D=4, and x%5B1%5D=2


m=%28-6%29%2F%284-2%29 Subtract -7 from -13 to get -6


m=%28-6%29%2F%282%29 Subtract 2 from 4 to get 2


m=-3 Reduce


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


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--7=-3%28x-2%29 Plug in m=-3, x%5B1%5D=2, and y%5B1%5D=-7


y%2B7=-3%28x-2%29 Rewrite y--7 as y%2B7


y%2B7=-3x%2B-3%28-2%29 Distribute


y%2B7=-3x%2B6 Multiply


y=-3x%2B6-7 Subtract 7 from both sides.


y=-3x-1 Combine like terms.



So the equation that goes through the points and is y=-3x-1


Notice how the graph of y=-3x-1 goes through the points and . So this visually verifies our answer.
Graph of y=-3x-1 through the points and

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim