SOLUTION: Write the equation of a line in slope-intercept form passing through (2, 7) and (-2, 9).

Algebra ->  Linear-equations -> SOLUTION: Write the equation of a line in slope-intercept form passing through (2, 7) and (-2, 9).      Log On


   

Question 506997: Write the equation of a line in slope-intercept form passing through (2, 7) and (-2, 9).
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=-2 and y%5B2%5D=9.


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


m=%289-7%29%2F%28-2-2%29 Plug in y%5B2%5D=9, y%5B1%5D=7, x%5B2%5D=-2, and x%5B1%5D=2


m=%282%29%2F%28-2-2%29 Subtract 7 from 9 to get 2


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


m=-1%2F2 Reduce


So the slope of the line that goes through the points and is m=-1%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-7=%28-1%2F2%29%28x-2%29 Plug in m=-1%2F2, x%5B1%5D=2, and y%5B1%5D=7


y-7=%28-1%2F2%29x%2B%28-1%2F2%29%28-2%29 Distribute


y-7=%28-1%2F2%29x%2B1 Multiply


y=%28-1%2F2%29x%2B1%2B7 Add 7 to both sides.


y=%28-1%2F2%29x%2B8 Combine like terms.


So the equation that goes through the points and is y=%28-1%2F2%29x%2B8


Notice how the graph of y=%28-1%2F2%29x%2B8 goes through the points and . So this visually verifies our answer.
Graph of y=%28-1%2F2%29x%2B8 through the points and


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim