Question

How do you graph `y + 1/3x = 2` by plotting points?

Answer 1

Please see below.

Explanation:

As the coefficient of `x` is `1/3`, let us pick three values of `x` which are multiple of `3` and let these be `-9,0` and `9`.

For these corresponding values of `y` will be

`y+1/3(-9)=2` or `y-3=2` or `y=5`

`y+1/3(0)=2` or `y=2`

`y+1/3(9)=2` or `y+3=2` or `y=-1`

Hence, three points through which `y+1/3x=2` passes are

`(-9,5)`, `(0,2)` and `(9,-1)`. Joining these points gives us the graph of `y+1/3x=2`

graph{y+1/3x=2 [-9.92, 10.08, -3.16, 6.84]}

Answer 2

For an equation like this you choose two values for x and calculate y, then trace the line between these two points.

Explanation:

Let me choose x=0 and x=6 just because I can. Plugging these values into the equation I get that when x=0 y=2 and when x=6 y=0.

Now remember that this only works for linear functions. Also, in this particular case, because of the division by 3, it is easy to see that choosing values for x that are multiples of 3 will be easier to calculate the results, so while you CAN choose any value for x to plot, choosing the values carefully will help with the calculations. Just as another example looking at the graph, I see that:
`if x=3` then `y=1`
`if x=9` then `y=-1`
and
`if x=-3` then `y=4`...

You can see the tho points (0,2) and (6,0) on the graph below
graph{y+1/3x=2 [-10, 10, -5, 5]}