Given the function below, fill in the table of values and use the table values to graph the function.
[tex]$y=3 x$[/tex]
\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline-3 & -9 \\
\hline-2 & -6 \\
\hline-1 & -3 \\
\hline 0 & 0 \\
\hline 1 & 3 \\
\hline 2 & 6 \\
\hline 3 & 9 \\
\hline
\end{tabular}
Answer (2)
Plot the points from the table on a coordinate plane.
Draw a straight line through the plotted points.
The line represents the graph of the function y = 3 x .
The graph is a straight line passing through the origin with a slope of 3. y = 3 x
Explanation
Understanding the Problem We are given the function y = 3 x and a table of values for x and y . Our goal is to use these values to graph the function.
Plotting the Points The table provides the following points: ( − 3 , − 9 ) , ( − 2 , − 6 ) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 2 , 6 ) , and ( 3 , 9 ) . We will plot these points on a coordinate plane.
Drawing the Line After plotting the points, we can draw a straight line that passes through all of them. This line represents the graph of the function y = 3 x .
Understanding the Graph The graph of y = 3 x is a straight line that passes through the origin ( 0 , 0 ) . For every increase of 1 in x , y increases by 3. This is because the slope of the line is 3.
Examples
Understanding linear functions like y = 3 x is crucial in many real-world scenarios. For instance, if you're earning 3 p er h o u r , t h e f u n c t i o n y = 3x m o d e l syo u r t o t a l e a r nin g s ( y ) ba se d o n t h e n u mb ero f h o u rsyo u w or k ( x$). Graphing this relationship helps you visualize how your earnings grow with each hour worked, making it easy to estimate your income for any given number of hours. This concept extends to various fields, such as calculating distances traveled at a constant speed or determining the cost of items bought at a fixed price per item.
To graph the function y = 3 x , first plot the points from the table on a coordinate plane. Draw a straight line through these points, showing that as x increases, y increases by 3 times as much. This graph demonstrates a linear relationship with a slope of 3 passing through the origin.
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