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

Jun 5, 2016

#### Explanation:

As the coefficient of $x$ is $\frac{1}{3}$, 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

$y + \frac{1}{3} \left(- 9\right) = 2$ or $y - 3 = 2$ or $y = 5$

$y + \frac{1}{3} \left(0\right) = 2$ or $y = 2$

$y + \frac{1}{3} \left(9\right) = 2$ or $y + 3 = 2$ or $y = - 1$

Hence, three points through which $y + \frac{1}{3} x = 2$ passes are

$\left(- 9 , 5\right)$, $\left(0 , 2\right)$ and $\left(9 , - 1\right)$. Joining these points gives us the graph of $y + \frac{1}{3} x = 2$

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

Jun 5, 2016

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:
$\mathmr{if} x = 3$ then $y = 1$
$\mathmr{if} x = 9$ then $y = - 1$
and
$\mathmr{if} x = - 3$ 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]}