SOLUTION: Write an equation in slope-intercept and standard form for a graph that passes through (-7,7) and (9,-1).

Algebra ->  Linear-equations -> SOLUTION: Write an equation in slope-intercept and standard form for a graph that passes through (-7,7) and (9,-1).      Log On


   

Question 228238: Write an equation in slope-intercept and standard form for a graph that passes through (-7,7) and (9,-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=-7 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=9 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=%28-1-7%29%2F%289--7%29 Plug in y%5B2%5D=-1, y%5B1%5D=7, x%5B2%5D=9, and x%5B1%5D=-7


m=%28-8%29%2F%289--7%29 Subtract 7 from -1 to get -8


m=%28-8%29%2F%2816%29 Subtract -7 from 9 to get 16


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--7%29 Plug in m=-1%2F2, x%5B1%5D=-7, and y%5B1%5D=7


y-7=%28-1%2F2%29%28x%2B7%29 Rewrite x--7 as x%2B7


y-7=%28-1%2F2%29x%2B%28-1%2F2%29%287%29 Distribute


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


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


y=%28-1%2F2%29x%2B7%2F2 Combine like terms.


So the equation that goes through the points and is y=%28-1%2F2%29x%2B7%2F2


Notice how the graph of y=%28-1%2F2%29x%2B7%2F2 goes through the points and . So this visually verifies our answer.
Graph of y=%28-1%2F2%29x%2B7%2F2 through the points and