To solve the equation [tex]\( x - y = 6 \)[/tex] and complete the table to find three ordered pair solutions, let's find the missing values based on the provided results.
1. First ordered pair:
Given [tex]\( y = 0 \)[/tex]:
[tex]\[
x - 0 = 6 \implies x = 6
\][/tex]
The first ordered pair is [tex]\( (6, 0) \)[/tex].
2. Second ordered pair:
Choose a new value for [tex]\( y \)[/tex]. Let's use [tex]\( y = 3 \)[/tex]:
[tex]\[
x - 3 = 6 \implies x = 6 + 3 = 9
\][/tex]
The second ordered pair is [tex]\( (9, 3) \)[/tex].
3. Third ordered pair:
Choose another value for [tex]\( y \)[/tex]. Let's use [tex]\( y = -2 \)[/tex]:
[tex]\[
x - (-2) = 6 \implies x = 6 - (-2) = 6 + 2 = 8
\][/tex]
The third ordered pair is [tex]\( (4, -2) \)[/tex].
So the completed table and ordered pairs are:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
6 & 0 \\
9 & 3 \\
4 & -2 \\
\hline
\end{array}
\][/tex]
Using any two of these ordered pairs, we can graph the equation [tex]\( x - y = 6 \)[/tex].
To graph:
1. Plot the points [tex]\((6, 0)\)[/tex] and [tex]\((9, 3)\)[/tex] on a coordinate plane.
2. Draw a straight line passing through these points, as they represent a linear relationship.
3. Verify that the point [tex]\((4, -2)\)[/tex] also lies on this line to ensure our solutions are correct.
This graph represents all the solutions to the equation [tex]\( x - y = 6 \)[/tex].
