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

Pick out at least 2 x values, find the resulting y values, plot them on a graph, then use a straight edge to connect them.

#### Explanation:

When we plot points, we need to find at least 2 x values and the corresponding y value - and then we can use a straight edge to connect the points.

With picking our x points, try to find ones that are easier to calculate. While any x value would be valid (25,657 is just as valid as 1 - they both will have a point on the line), it will be easier to calculate and graph some numbers rather than others.

One of my favourites is $x = 0$. So let's do that. When $x = 0$:

$y = - 3 x + 2$
$y = - 3 \left(0\right) + 2$
$y = 2$

So that's one plot point - $\left(0 , 2\right)$ Let's do another. How about $x = 1$

$y = - 3 \left(1\right) + 2$
$y = - 3 + 2$
$y = - 1$

So that's another plot point - $\left(1 , - 1\right)$.

If you need a table of plot points, you can pick out 2 or 3 more x values, and numbers like $2 , - 1 , \mathmr{and} - 2$ would be good candidates (and if you want to get fancy, fractions with a 3 in the denominator would be good because they would cancel against the 3 in the x-term, like this example of $x = \frac{1}{3}$):

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

Plot them out and get:

graph{-3x+2 [-5, 5, -5, 5]}

(each line of the graph paper is each value 1 (so you move 5 lines to the right to get to the 5 on the x axis), and the horizontal line is x while the vertical line is y). Our first point, (0,2), can be found by going 0 spaces across on the x axis and 2 up on the y axis. Our next point, (1,-1), can be found by going 1 to the right on the x axis and 1 down on the y axis.

And remember that each value on our plot of the solution is a valid answer. So if you wanted to try to plot $x = - \frac{11}{245345}$, you can and the point will sit on the plot very very close to our first plot point of (0,2).