find the intercepts and use them to graph the equation y= 3x+3

Thanks Heuraka, I am going to take a different path.  

y= 3x+3

The y intercept is where x=0    so 3x=0    put your finger over 3x you don't need that bit!

y=3

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The x intercept is where y=0  so you have to solve

0=3x+3

-3=3x

x=-1

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Now you have your 2 intercepts it is really easy to graph.   

find the intercepts and use them to graph the equation

$$\begin{array}{rcl} y & = & 3x+3 \quad | \quad -3x\\ \\ y-3x &=& 3 \quad | \quad :3\\ \\ \frac{y-3x}{3} &=&1\\\\ \frac{y}{3} + \frac{-3x}{3} &=&1\\\\ \frac{y}{3} + \frac{-x}{1} &=&1\\\\ \frac{y}{3} + \frac{x}{-1} &=&1\\\\ \frac{x}{-1} + \frac{y}{3} &=&1 \end{array}$$

$$\boxed{\dfrac{x}{ x_{intercept} } + \dfrac{y}{ y_{intercept} } &=&1 }\\\\ x_{intercept} = -1\\ y_{intercept} = 3$$