Given the function below, fill in the table of values and use the table values to graph.
[tex]y=x+5[/tex]
\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y=x+5$[/tex] \\
\hline-3 & \\
\hline-2 & \\
\hline-1 & \\
\hline 0 & \\
\hline 1 & \\
\hline 2 & \\
\hline 3 & \\
\hline
\end{tabular}
Answer (2)
Calculate y for each x value using y = x + 5 .
For x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , the corresponding y values are 2 , 3 , 4 , 5 , 6 , 7 , 8 .
Plot the points ( − 3 , 2 ) , ( − 2 , 3 ) , ( − 1 , 4 ) , ( 0 , 5 ) , ( 1 , 6 ) , ( 2 , 7 ) , ( 3 , 8 ) on a coordinate plane.
Draw a straight line through the points to graph the function y = x + 5 .
Explanation
Understanding the Problem We are given the function y = x + 5 and asked to complete a table of values and then graph the function using those values.
Calculating the Table Values First, we need to calculate the y values for each given x value using the function y = x + 5 .
Calculating y for x = -3 For x = − 3 , we have y = − 3 + 5 = 2 .
Calculating y for x = -2 For x = − 2 , we have y = − 2 + 5 = 3 .
Calculating y for x = -1 For x = − 1 , we have y = − 1 + 5 = 4 .
Calculating y for x = 0 For x = 0 , we have y = 0 + 5 = 5 .
Calculating y for x = 1 For x = 1 , we have y = 1 + 5 = 6 .
Calculating y for x = 2 For x = 2 , we have y = 2 + 5 = 7 .
Calculating y for x = 3 For x = 3 , we have y = 3 + 5 = 8 .
Completing the Table and Graphing Now we can fill in the table with the calculated y values:
x
y = x + 5
-3
2
-2
3
-1
4
0
5
1
6
2
7
3
8
These points can be plotted on a coordinate plane, and a straight line can be drawn through them to represent the graph of the function y = x + 5 .
Examples
Understanding linear functions like y = x + 5 is crucial in many real-world scenarios. For instance, imagine you're saving money. If you start with $5 and save 1 e a c h d a y , t h e t o t a l am o u n t yo u ha v ec anb ere p rese n t e d b y t h e f u n c t i o n y = x + 5 , w h ere x$ is the number of days. By understanding this linear relationship, you can easily predict how much money you'll have after a certain number of days. This concept extends to various fields, such as calculating the cost of services with a fixed initial fee plus a per-unit charge, or modeling simple growth patterns.
To find the values of y from the function y = x + 5 , we calculated it for various x values and completed the table. We plotted the points on a coordinate plane and drew a straight line to represent the graph of the function. This function is linear with a constant slope of 1 and a y-intercept of 5.
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