Question

How do you graph the equation `y=-3x+2`?

Answer 1

See below:

Explanation:

This equation is in slope-intercept form, which is my favourite for graphing lines.

The slope-intercept form is in the general form of:

`y=mx+b`

where `m` is the slope and `b` is the `y`-intercept.

Let's graph the `y`-intercept first.

The `y`-intercept is 2. This means that that point is `(0,2)`. So let's graph that:

graph{(x-0)^2+(y-2)^2-.3^2=0}

So that's one point. Now let's plot another point (and then we can use a straightedge to join them).

The slope is `-3`. Slope is calculated by `"rise"/"run"` - in other words the change in `y` divided by the change in `x`. In this case, we will drop 3 spots for every 1 spot we move right. So that point is `(0+1, 2-3)=(1,-1)`. Let's graph that:

graph{((x-0)^2+(y-2)^2-.3^2)((x-1)^2+(y+1)^2-.3^2)=0}

And now connect them up!

graph{((x-0)^2+(y-2)^2-.3^2)((x-1)^2+(y+1)^2-.3^2)(y+3x-2)=0}