Copy and complete the table of values for $y=4x$. What values should replace $A, B, C$ and $D$?
\begin{tabular}{c|c|c|c|c}
$x$ & -1 & 0 & 1 & 2 \\
\hline
$y$ & A & B & C & D
\end{tabular}
Answer (2)
Substitute x = − 1 into y = 4 x to find A = 4 ( − 1 ) = − 4 .
Substitute x = 0 into y = 4 x to find B = 4 ( 0 ) = 0 .
Substitute x = 1 into y = 4 x to find C = 4 ( 1 ) = 4 .
Substitute x = 2 into y = 4 x to find D = 4 ( 2 ) = 8 .
Therefore, the values are A = − 4 , B = 0 , C = 4 , D = 8 .
Explanation
Understanding the Problem We are given the equation y = 4 x and a table of x values. We need to find the corresponding y values for each x value.
Calculating A To find the value of A, we substitute x = − 1 into the equation y = 4 x :
A = 4 ( − 1 ) = − 4 So, A = − 4 .
Calculating B To find the value of B, we substitute x = 0 into the equation y = 4 x :
B = 4 ( 0 ) = 0 So, B = 0 .
Calculating C To find the value of C, we substitute x = 1 into the equation y = 4 x :
C = 4 ( 1 ) = 4 So, C = 4 .
Calculating D To find the value of D, we substitute x = 2 into the equation y = 4 x :
D = 4 ( 2 ) = 8 So, D = 8 .
Final Answer Therefore, the values are A = − 4 , B = 0 , C = 4 , and D = 8 .
Examples
Understanding linear relationships like y = 4 x is crucial in many real-world scenarios. For instance, if you're saving money at a rate of 4 p er w ee k , t hi se q u a t i o nm o d e l syo u rs a v in g s ( y ) a f t er x w ee k s . 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 ere q u a l s 100 ce n t im e t ers , t h ee q u a t i o n w o u l d b e y = 100x$. These simple linear equations help us predict outcomes and plan accordingly in everyday situations.
To find the values in the table for the equation y = 4 x , we calculated: A = − 4 , B = 0 , C = 4 , D = 8 . The complete table is x : [ − 1 , 0 , 1 , 2 ] , y : [ − 4 , 0 , 4 , 8 ] .
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