Complete the table.

\begin{tabular}{|c|c|}
\hline$x$ & $y=5 x$ \\
\hline-3 & 1 \\
\hline-2 & \\
\hline-1 & \\
\hline 0 & \\
\hline 1 & \\
\hline 2 & \\
\hline 3 & \\
\hline
\end{tabular}

The problem involves finding y values for a linear equation y = 5 x given different x values.
Calculate y for x = − 3 : y = 5 × ( − 3 ) = − 15 .
Calculate y for x = − 2 , − 1 , 0 , 1 , 2 , 3 using the same equation.
The completed y values are: -15, -10, -5, 0, 5, 10, 15, so the final answer is − 15 , − 10 , − 5 , 0 , 5 , 10 , 15 ​ .

Explanation

Understanding the Problem We are given a table with x values and a corresponding y value defined by the equation y = 5 x . We need to complete the table by finding the correct y values for the given x values.

Correcting the Initial Value For x = − 3 , the given y value is incorrect. The correct value is y = 5 × ( − 3 ) = − 15 .

Calculating Remaining y Values Now, let's calculate the y values for the remaining x values:


For x = − 2 , y = 5 × ( − 2 ) = − 10 .
For x = − 1 , y = 5 × ( − 1 ) = − 5 .
For x = 0 , y = 5 × 0 = 0 .
For x = 1 , y = 5 × 1 = 5 .
For x = 2 , y = 5 × 2 = 10 .
For x = 3 , y = 5 × 3 = 15 .

Completed Table So, the completed table is:




x
y = 5 x



-3
-15


-2
-10


-1
-5


0
0


1
5


2
10


3
15



Final Answer The y values for the given x values are -15, -10, -5, 0, 5, 10, and 15.

Examples
Understanding linear relationships like y = 5 x is crucial in many real-world scenarios. For instance, if you're saving money at a rate of 5 p er d a y , t h ee q u a t i o n y = 5x m o d e l syo u r t o t a l s a v in g s ( y ) a f t er x d a ys . S imi l a r l y , i f yo u ′ reco n v er t in g m e t ers t oce n t im e t ers ( w h ere 1 m e t er = 100 ce n t im e t ers ) , t h ere l a t i o n s hi p i s l in e a r : y = 100x , w h ere y i s t h e l e n g t hin ce n t im e t ers an d x$ is the length in meters. Recognizing and using these linear relationships helps in making predictions and understanding proportional changes.

Answered by GinnyAnswer | 2025-07-08