How do you graph `y=x/3+1`?

It's linear as you see the power of `x` first degree

GET

x-intercept when y=0

`x=-3`

`(-3,0)`

y-intercept when x=0

`y=1`

`(0,1)`

SO,

Take the two point and draw a straight line.

`" "`
Given:

Linear equation `color(red)(y = x/3 + 1`

Steps:

(1) Graph the Parent Function: `color(blue)(y=x`

(2) Graph the function `color(green)(y=x/3`

(3) Graph the given function `color(red)(y=x/3 + 1`

(4) Reflection

`color(black)("Step 1"`

Graph the Parent Function: `color(blue)(y=x`

Observe that the linear equation goes through the origin `(0,0)`

`color(black)("Step 2"`

Graph the function `color(green)(y=x/3`

Observe that the linear equation goes through the origin `(0,0)` as well similar to the parent function.

`color(black)("Step 3"`

Graph the given function `color(red)(y=x/3 + 1`

Observe the following:

(a) x-intercept is at `(-3,0)`

(b) y-intercept is at `(0,1)`

`color(black)("Step 4"`

We will view all the graphs together and reflect on the behavior of the given function `color(red)(y = x/3 + 1`.

Reflection:

(a) Graph of the function `color(green)(y=x/3` and the graph the given function `color(red)(y=x/3 + 1` form parallel lines.

(b) Graph of the given function `color(red)(y=x/3 + 1` is a vertical shift of `"1 unit"` on the y-axis from the origin: `(0,0)`.

Hope you find this solution helpful.