# How do you graph y=-6+2x using the intercepts?

Jun 7, 2016

$\textcolor{b l u e}{\implies {y}_{\text{intercept}} \to \left(x , y\right) = \left(0 , - 6\right)}$

$\textcolor{b l u e}{\implies {x}_{\text{intercept}} \to \left(x , y\right) = \left(3 , 0\right)}$

#### Explanation:

Find the points of intercepts and draw a line through them.

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$\textcolor{b l u e}{\text{Determine the "x" intercept}}$

The line crosses the x-axis at $y = 0$ so by substitution we have:

$\textcolor{b r o w n}{y = 2 x - 6} \textcolor{g r e e n}{\text{ "->" } 0 = 2 x - 6}$

Add 6 to both side so that the 6 on the right becomes 0

$6 = 2 x + 0$

Divide both sides by 2 so that the 2 from $2 x$ becomes 1. This is because $1 \times x = x$. That is, you get rid of the 2 on the right.

$\frac{6}{2} = \frac{2}{2} \times x$

$3 = x$

$\textcolor{b l u e}{\implies {x}_{\text{intercept}} \to \left(x , y\right) = \left(3 , 0\right)}$

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$\textcolor{b l u e}{\text{Determine the "y" intercept}}$

The line crosses the y-axis at $x = 0$ so by substitution we have:

$\textcolor{b r o w n}{y = 2 x - 6} \textcolor{g r e e n}{\text{ "->" } y = 2 \left(0\right) - 6}$

But $2 \times 0 = 0$

$y = 0 - 6$

$y = - 6$

$\textcolor{b l u e}{\implies {y}_{\text{intercept}} \to \left(x , y\right) = \left(0 , - 6\right)}$
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