SOLUTION: Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.

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Question 536614: Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.
Found 2 solutions by jim_thompson5910, Alan3354:
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=5 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=8.


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


m=%288-4%29%2F%287-5%29 Plug in y%5B2%5D=8, y%5B1%5D=4, x%5B2%5D=7, and x%5B1%5D=5


m=%284%29%2F%287-5%29 Subtract 4 from 8 to get 4


m=%284%29%2F%282%29 Subtract 5 from 7 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-4=2%28x-5%29 Plug in m=2, x%5B1%5D=5, and y%5B1%5D=4


y-4=2x%2B2%28-5%29 Distribute


y-4=2x-10 Multiply


y=2x-10%2B4 Add 4 to both sides.


y=2x-6 Combine like terms.


y=2x-6 Simplify


So the equation that goes through the points and is y=2x-6


Notice how the graph of y=2x-6 goes through the points and . So this visually verifies our answer.
Graph of y=2x-6 through the points and


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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.
--------------
|x y 1|
|5 4 1| = 0
|7 8 1|
--------
x*(4-8) - y*(5-7) + (40-28) = 0
-4x + 2y + 12 = 0
2x - y = 6 (standard form)
y = 2x - 6 (slope intercept form)