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

Jun 7, 2016

First get the equation into standard form:
$y = - \frac{3}{5} x + \frac{12}{5}$

Then, start plugging in values for $x$ and plotting points.

#### Explanation:

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 $3 x$ from each side. This gives you:

$5 y = - 3 x + 12$.

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

$y = \frac{- 3 x + 12}{5}$

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:

$y = \frac{- 3 \left(1\right) + 12}{5}$

Work that out... $- 3 + 12 = 9$, $\frac{9}{5} = 1 \frac{4}{5}$. So you have your first coordinate, $\left(1 , 1 \frac{4}{5}\right)$.

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

$y = \frac{- 3 \left(4\right) + 12}{5}$

Well, $- 3 \cdot 4 = 0$, and $\frac{0}{5} = 0$, so your coordinate is $\left(4 , 0\right)$. 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]}

Jun 7, 2016

Express the equation in the point-slope form, i.e, y = mx + c.

#### Explanation:

$3 x + 5 y = 12$

$5 y = - 3 x + 12$

$y = - \frac{3}{5} \cdot x + \frac{12}{5}$

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 $x = 0 , y = \frac{12}{5}$

when $x = 1 , y = \frac{9}{5}$

when $x = - 1 , y = \frac{15}{5} = 3$

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