SOLUTION: graph 3x + 2y = 6. Where do you begin? Explain

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Question 208161: graph 3x + 2y = 6. Where do you begin? Explain
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
There are two ways to do this (actually there are more, but I'm only showing two here).

Method #1

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since 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

Also, because the slope is , this means:

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

So starting at , go down 3 units

and to the right 2 units to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points and

OR....

Method #2

To plot , we can use the x and y intercepts.

x-intercept

To find the x-intercept, plug in and solve for x

Start with the given equation.

Plug in .

Multiply and 0 to get 0.

Simplify.

Multiply.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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y-intercept

To find the y-intercept, plug in and solve for y

Start with the given equation.

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

Now plot the x and y intercepts:

Now draw a line through the points to graph the equation

Graph of