How do you graph the equation by plotting points `3x + 5y = 12`?

Getting the equation to standard form

It will be much easier to plug in values if the equation is in standard form (so that `y` is isolated). First, subtract `3x` from each side. This gives you:

`5y = -3x + 12`.

Next, divide each side by 5 to isolate `y`.

`y = (-3x +12)/5`

You can do the distributive property to get it to truly standard form, but it'll be pretty easier from here.

Pluggin' in values

I always find it helps to make a table, but however you want, find a way to record. Pick a simple value for `x`. Let's say 1. Your equation would look like this:

`y = (-3(1) +12)/5`

Work that out... `-3 + 12 = 9`, `9 / 5 = 1 4/5`. So you have your first coordinate, `(1, 1 4/5)`.

Try another! Let's have `x = 4`. So...

`y = (-3(4) +12)/5`

Well, `-3 * 4 = 0`, and `0/5 = 0`, so your coordinate is `(4, 0)`. Now that you have two points, plot them on a graph, and draw a line connecting them!
graph{y = (-3x +12)/5 [-8.89, 8.89, -4.444, 4.445]}

`3x + 5y = 12`

`5y = -3x + 12`

`y = -3/5*x +12/5`

Now put values of x in the equation and get corresponding values of y. Plot the graph according to the values you get.

For example :

when `x = 0, y = 12/5`

when `x = 1, y = 9/5`

when `x = -1, y = 15/5 = 3`

graph{(-3/5)*x+12/5 [-7.174, 6.87, -1.386, 5.644]}