SOLUTION: What would a graph of 2x+3y=6 look like?

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Question 169796: What would a graph of 2x+3y=6 look like?
Found 2 solutions by jim_thompson5910, jojo14344:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 2x%2B3y=6, we first need to solve for y


2x%2B3y=6 Start with the given equation.


3y=6-2x Subtract 2x from both sides.


3y=-2x%2B6 Rearrange the terms.


y=%28-2x%2B6%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%28-2%29%2F%283%29%29x%2B%286%29%2F%283%29 Break up the fraction.


y=-%282%2F3%29x%2B2 Reduce.




Looking at y=-%282%2F3%29x%2B2 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-2%2F3 and the y-intercept is b=2


Since b=2 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -2%2F3, this means:

rise%2Frun=-2%2F3


which shows us that the rise is -2 and the run is 3. This means that to go from point to point, we can go down 2 and over 3



So starting at , go down 2 units


and to the right 3 units to get to the next point



Now draw a line through these points to graph y=-%282%2F3%29x%2B2

So this is the graph of y=-%282%2F3%29x%2B2 through the points and

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B3y=6
To get the slope and Y=intercept:
y=mx%2Bb
3y=-2x%2B6
cross%283%29y%2Fcross%283%29=%28-2x%2B6%29%2F3
y=%28-2%2F3%29x%2B%286%2F3%29----> y=%28-2%2F3%29x%2B2
See graph,

Thank you,
Jojo