From simple questions to complex issues, IDNLearn.com has the answers you need. Find the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
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].
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].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.
