# How do you graph the line y=2x+2?

Jul 20, 2017

See explanation

#### Explanation:

The minimum number of points needed to draw a strait line graph is 2. However, 3 is better as one of them forms a check. They should all line up. If not then something is wrong.

Lets determine 2 points

The line will 'cross' the y axis at $x = 0$ and cross the x axis at $y = 0$
So we can determine these points (intercepts) by substitution.
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For y-intercept set $\textcolor{red}{x = 0}$ giving:

$y = \text{ } 2 x \textcolor{w h i t e}{. .} + 2$
$\textcolor{g r e e n}{y = \left(2 \textcolor{red}{\times 0}\right) + 2 \text{ "->" } y = 2}$

So y-intercept is at the point $\left(x , y\right) = \left(0 , 2\right)$
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For x-intercept set $\textcolor{red}{y = 0}$ giving:

$\textcolor{g r e e n}{\textcolor{red}{0} = 2 x + 2}$

Subtract $\textcolor{red}{2}$ from both sides

$\textcolor{g r e e n}{0 \textcolor{red}{- 2} \text{ "=" } 2 x + 2 \textcolor{red}{- 2}}$

$- 2 \text{ "=" } 2 x + 0$

Divide both sides by $\textcolor{red}{2}$

color(green)((-2)/(color(red)(2))" "=" "2/(color(red)(2))xx x

But $\frac{- 2}{2} = - 1 \mathmr{and} \frac{2}{2} = + 1$

$- 1 \text{ "=" } x$

So the y-intercept is at the point $\left(x , y\right) = \left(- 1 , 0\right)$
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Mark and label these two points then draw you line through them. Take the line to the edges of the graphing area on the paper.
Do not forget to label your graph.

In an exam you get extra marks for labelling you points and giving a title to your graph.