How do you graph `y=3/2 x + 3`?

The equation is in the slope intercept form which makes this easy

`y = mx + b`

where m = the slope ( think mountain ski slope)
and b = the y intercept ( think beginning.)

Start at b the beginning

b = ( 0 +3) b is the y intercept where x = 0 and y = 3

Then use the slope `2/3 = y/x`

Add 2 to the y value `3 + 2 = 5`
Add 3 to the x value `0 + 3 = 3`

this gives the second point ( 3,5)

plot the two points and connect the dots with a line, The graph of the equation is done.

Graph:

`y=3/2x+3`

You need two points to graph a straight line. The x- and y-intercepts are easiest to find, especially when the equation is in standard form.

Convert to standard form, `Ax+By=C`, by subtracting `3/2x` from both sides.

`-3/2x+y=3`

X-intercept: value of `x` when `y=0`

Substitute `0` for `y` and solve for `x`.

`-3/2x+0=3`

`-3/2x=3`

Multiply both sides by `2`.

`-3x=3xx2`

`-3x=6`

Divide both sides by `-3`.

`x=6/(-3)`

`x=-2`

The x-intercept is: `(-2,0)`.

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x` and solve for `y`.

`-3/2(0)+y=3`

`y=3`

The y-intercept is: `(0,3)`.

Plot the x- and y-intercept and draw a straight line through them.

graph{y=3/2x+3 [-10, 10, -5, 5]}