SOLUTION: y=2x-4 y=6x+4 and i need help graphing it with a sketch of the graph

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Question 970918: y=2x-4
y=6x+4
and i need help graphing it with a sketch of the graph
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-4
y=6x+4
The first has a slope of +2 and crosses the y-axis at -4.
The second has a steeper slope of +6 and crosses the y-axis at +4
Both go to the right 1 unit; one goes up only 2 units, the other 6 units..
+graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x-4%2C6x%2B4%29



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if you have two equations of the line, to sketch a graph you need two points
y=2x-4
make a table:
x|y
0|-4...y=2%2A0-4=>y=-4
2|0...0=2x-4=>2x=4=>x=2
plot points and draw a line through

do same with
y=6x%2B4
x|y
0|4...y=6%2A0%2B4=>y=4
-2%2F3|0...0=6x%2B4=>6x=-4=>x=-4%2F6=>x=-2%2F3

plot points and draw a line through



but, if you are given a system to solve, then you need to do it this way:
y=2x-4
y=6x%2B4
------------------write in standard form first

-2x%2By=-4
-6x%2By=4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-2x%2By=-4

-6x%2By=4





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=-4 Start with the given equation



1y=-4%2B2x Add 2+x to both sides



1y=%2B2x-4 Rearrange the equation



y=%28%2B2x-4%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=2x-4 Reduce



Now lets graph y=2x-4 (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-4%29+ Graph of y=2x-4




So let's solve for y on the second equation


-6x%2By=4 Start with the given equation



1y=4%2B6x Add 6+x to both sides



1y=%2B6x%2B4 Rearrange the equation



y=%28%2B6x%2B4%29%2F%281%29 Divide both sides by 1



y=%28%2B6%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=6x%2B4 Reduce





Now lets add the graph of y=6x%2B4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C6x%2B4%29+ Graph of y=2x-4(red) and y=6x%2B4(green)


From the graph, we can see that the two lines intersect at the point (-2,-8) (note: you might have to adjust the window to see the intersection)