SOLUTION: Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line. (-1,4), (6,4)

Algebra ->  Linear-equations -> SOLUTION: Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line. (-1,4), (6,4)      Log On


   

Question 637275: Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
(-1,4), (6,4)
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=-1 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=4.


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


m=%284-4%29%2F%286--1%29 Plug in y%5B2%5D=4, y%5B1%5D=4, x%5B2%5D=6, and x%5B1%5D=-1


m=%280%29%2F%286--1%29 Subtract 4 from 4 to get 0


m=%280%29%2F%287%29 Subtract -1 from 6 to get 7


m=0 Reduce


So the slope of the line that goes through the points and is m=0


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=0%28x--1%29 Plug in m=0, x%5B1%5D=-1, and y%5B1%5D=4


y-4=0%28x%2B1%29 Rewrite x--1 as x%2B1


y-4=0x%2B0%281%29 Distribute


y-4=0x%2B0 Multiply


y=0x%2B0%2B4 Add 4 to both sides.


y=0x%2B4 Combine like terms.


y=4 Simplify


So the equation that goes through the points and is y=%2B4


Notice how the graph of y=4 goes through the points and . So this visually verifies our answer.
Graph of y=4 through the points and