SOLUTION: Can you graph the following? y=2x+1 y=2/3x+1 Thanks for your help

Algebra ->  Graphs -> SOLUTION: Can you graph the following? y=2x+1 y=2/3x+1 Thanks for your help      Log On


   

Question 119743: Can you graph the following?
y=2x+1


y=2/3x+1
Thanks for your help
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=2x%2B1...slope-intercept form
-+2x+%2B+y=1.....standard form


y=%282%2F3%29x%2B1...slope-intercept form
-+%282%2F3%29x+%2B+y=1.....standard form


Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the second equation %28-2%2F3%29x%2By=1


3%28%28-2%2F3%29x%2By%29=3%281%29 Multiply both sides of the second equation by the LCD 3



-2x%2B3y=1 Distribute



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So our new system of equations is:


-2x%2By=1

-2x%2B3y=1





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


-2x%2By=1 Start with the given equation



1y=1%2B2x Add 2+x to both sides



1y=%2B2x%2B1 Rearrange the equation



y=%28%2B2x%2B1%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=2x%2B1 Reduce



Now lets graph y=2x%2B1 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B1%29+ Graph of y=2x%2B1




So let's solve for y on the second equation


-2x%2B3y=1 Start with the given equation



3y=1%2B2x Add 2+x to both sides



3y=%2B2x%2B1 Rearrange the equation



y=%28%2B2x%2B1%29%2F%283%29 Divide both sides by 3



y=%28%2B2%2F3%29x%2B%281%29%2F%283%29 Break up the fraction



y=%282%2F3%29x%2B1%2F3 Reduce





Now lets add the graph of y=%282%2F3%29x%2B1%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B1%2C%282%2F3%29x%2B1%2F3%29+ Graph of y=2x%2B1(red) and y=%282%2F3%29x%2B1%2F3(green)


From the graph, we can see that the two lines intersect at the point (-1%2F2,0) (note: you might have to adjust the window to see the intersection)