SOLUTION: How do you write the equation of a line in slope-intercept form passing through (4,5) and (6,8)?

Algebra ->  Linear-equations -> SOLUTION: How do you write the equation of a line in slope-intercept form passing through (4,5) and (6,8)?      Log On


   

Question 552785: How do you write the equation of a line in slope-intercept form passing through (4,5) and (6,8)?
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=5.
Also, is the second point . So this means that x%5B2%5D=6 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=%288-5%29%2F%286-4%29 Plug in y%5B2%5D=8, y%5B1%5D=5, x%5B2%5D=6, and x%5B1%5D=4


m=%283%29%2F%286-4%29 Subtract 5 from 8 to get 3


m=%283%29%2F%282%29 Subtract 4 from 6 to get 2


So the slope of the line that goes through the points and is m=3%2F2


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-5=%283%2F2%29%28x-4%29 Plug in m=3%2F2, x%5B1%5D=4, and y%5B1%5D=5


y-5=%283%2F2%29x%2B%283%2F2%29%28-4%29 Distribute


y-5=%283%2F2%29x-6 Multiply


y=%283%2F2%29x-6%2B5 Add 5 to both sides.


y=%283%2F2%29x-1 Combine like terms.


y=%283%2F2%29x-1 Simplify


So the equation that goes through the points and is y=%283%2F2%29x-1


Notice how the graph of y=%283%2F2%29x-1 goes through the points and . So this visually verifies our answer.
Graph of y=%283%2F2%29x-1 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