# How do you graph the line  y=-3x+3?

Dec 18, 2016

Wee explanation

#### Explanation:

$\textcolor{b l u e}{\text{Main Method :}}$

Determine 2 separate points which are marked on the graph paper then draw a line through them.
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$\textcolor{p u r p \le}{\text{Method 1}}$

Substitute any sensible values into $x$ and se what value of $y$ you get. Then plot the points with a line going through them.

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$\textcolor{p u r p \le}{\text{Method 2 - more about teaching algebra}}$

$\textcolor{b l u e}{\text{Determine the point where } x = 0}$

Substitute 0 wherever $x$ is

$y = - 3 x + 3 \text{ "->" } y = - 3 \left(0\right) + 3$

but $0 \times \left(- 3\right) = 0$ giving:

$y = 0 + 3$

So at $x = 0 \text{ } y$ takes on the value of 3

So point 1 $\to {P}_{1} \to \left(x , y\right) = \left(0 , 3\right)$
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$\textcolor{b l u e}{\text{Determine the point where } y = 0}$

Substitute 0 wherever $y$ is:

$y = - 3 x + 3 \text{ "->" } 0 = - 3 x + 3$

Add $3 x$ to both sides

$0 + 3 x = - 3 x + 3 x + 3$

but $- 3 x + 3 x = 0$

$3 x = 0 + 3$

Divide both sides by 3

$\frac{3}{3} x = \frac{3}{3}$

But $\frac{3}{3} = 1$

$x = 1$

So point 2 $\to {P}_{2} \to \left(x , y\right) = \left(1 , 0\right)$
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