Sure, let's plot the ordered pairs for the given linear function [tex]\( y = -2x - 5 \)[/tex] and the provided domain [tex]\( D = \{-6, -5, -2, 0, 1\} \)[/tex].
1. Identifying the Ordered Pairs: Given the function [tex]\( y = -2x - 5 \)[/tex], we need to substitute each value of [tex]\( x \)[/tex] from the domain [tex]\( D \)[/tex] into the function to find the corresponding [tex]\( y \)[/tex]-values. Here are the calculations:
- For [tex]\( x = -6 \)[/tex]:
[tex]\[
y = -2(-6) - 5 = 12 - 5 = 7
\][/tex]
So, the ordered pair is [tex]\((-6, 7)\)[/tex].
- For [tex]\( x = -5 \)[/tex]:
[tex]\[
y = -2(-5) - 5 = 10 - 5 = 5
\][/tex]
So, the ordered pair is [tex]\((-5, 5)\)[/tex].
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -2(-2) - 5 = 4 - 5 = -1
\][/tex]
So, the ordered pair is [tex]\((-2, -1)\)[/tex].
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -2(0) - 5 = 0 - 5 = -5
\][/tex]
So, the ordered pair is [tex]\((0, -5)\)[/tex].
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -2(1) - 5 = -2 - 5 = -7
\][/tex]
So, the ordered pair is [tex]\((1, -7)\)[/tex].
2. Plotting the Ordered Pairs: Now, let's plot these points on a graph.
- The point [tex]\((-6, 7)\)[/tex] is located at -6 on the [tex]\( x \)[/tex]-axis and 7 on the [tex]\( y \)[/tex]-axis.
- The point [tex]\((-5, 5)\)[/tex] is located at -5 on the [tex]\( x \)[/tex]-axis and 5 on the [tex]\( y \)[/tex]-axis.
- The point [tex]\((-2, -1)\)[/tex] is located at -2 on the [tex]\( x \)[/tex]-axis and -1 on the [tex]\( y \)[/tex]-axis.
- The point [tex]\((0, -5)\)[/tex] is located at 0 on the [tex]\( x \)[/tex]-axis and -5 on the [tex]\( y \)[/tex]-axis.
- The point [tex]\((1, -7)\)[/tex] is located at 1 on the [tex]\( x \)[/tex]-axis and -7 on the [tex]\( y \)[/tex]-axis.
3. Drawing the Linear Function: After plotting all these points on the graph, draw a straight line through them. Since the function [tex]\( y = -2x - 5 \)[/tex] is linear, all the points should lie on a straight line.
Here's a brief summary in tabular form for clarity:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 7 \\
-5 & 5 \\
-2 & -1 \\
0 & -5 \\
1 & -7 \\
\hline
\end{array}
\][/tex]
Plot these points on your graph paper, connect them with a straight line, and you will have the graphical representation of the function [tex]\( y = -2x - 5 \)[/tex] for the given domain [tex]\( D \)[/tex].
