How do you graph the line x-y=2?

Apr 6, 2016

See explanation

Explanation:

Given:$\text{ } \textcolor{b r o w n}{x - y = 2}$

$\textcolor{g r e e n}{\text{Step 1: Rearrange the equation into standard form}}$

Add $\textcolor{b l u e}{y}$ to both sides

$\textcolor{b r o w n}{x - y \textcolor{b l u e}{+ y} = 2 \textcolor{b l u e}{+ y}}$

$\implies x + 0 = 2 + y$

Subtract $\textcolor{b l u e}{2}$ from both sides

$\implies \textcolor{b r o w n}{x \textcolor{b l u e}{- 2} = 2 \textcolor{b l u e}{- 2} + y}$

$\implies x - 2 = 0 + y$

$\textcolor{g r e e n}{y = x - 2}$

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$\textcolor{g r e e n}{\text{Step 2: Build data so that graph can be plotted}}$
Selecting values for $x$ at random

Let $x = - 1 \text{ then } y = - 1 - 2 = - 3$

Let $x = 0 \text{ then } y = 0 - 2 = - 2$

Let $x = 2 \text{ then } y = 2 - 2 = 0$

We now have three sets of point

Point ${P}_{1} \to \left(x , y\right) \to \left(- 1 , - 3\right)$
Point ${P}_{2} \to \left(x , y\right) \to \left(0 , - 2\right)$
Point ${P}_{2} \to \left(x , y\right) \to \left(2 , 0\right)$

Mark these point on graph paper and draw a line through them extending it to the edges of the scales. If all three dots must line up. If not then there is an error some where. 3 dots are better than just 2 as they form a check.

Your graph should look something like this: 