Question

How do you find the slope of `3y=x+3`?

Answer 1

Slope: `1/3`

Explanation:

Slope-intercept form: `y=mx+b`; where `m` is the slope.

If we put the given equation into slope-intercept form, we can identify the slope.

First get `y` all by itself.

`3y = x+3`

`y = x/3 + 1`

This equation is now in slope intercept form. We must find the slope. We saw at the top that the slope, `m`, comes right before the variable. Here is our variable term:

`x/3`

It is in the form of a fraction. What do we do to clearly identify the slope? Rewrite the variable term, since `x/3` is the same as `1/3 times x`.

`x/3 = 1/3 times x = 1/3 x`

Now let's rewrite the whole equation.

`y = 1/3 x + 1`

`color(grey)(y = mx+b)`

Look for the number before `x`, or the number combined with it. In this case, the slope appears to be `1/3`.

If we were to graph the equation and look at the slope that way, it would be the same.

graph{1/3x+1 [-10, 10, -5, 5]}