Copy and complete the table of values for [tex]$y=2 x+1$[/tex]. What values should replace A and B?
[tex]
\begin{tabular}{c|c|c|c|c|c}
$x$ & -1 & 0 & 1 & 2 & 3 \\
\hline
$y$ & -1 & A & 3 & B & 7
\end{tabular}
[/tex]
Answer (2)
Substitute x = 0 into y = 2 x + 1 to find A.
Calculate A = 2 ( 0 ) + 1 = 1 .
Substitute x = 2 into y = 2 x + 1 to find B.
Calculate B = 2 ( 2 ) + 1 = 5 .
The values that should replace A and B are 1 , 5 .
Explanation
Understanding the Problem We are given the equation y = 2 x + 1 and a table of x and y values. We need to find the values of A and B in the table.
Finding A To find the value of A, we substitute x = 0 into the equation y = 2 x + 1 .
Calculating A A = 2 ( 0 ) + 1 = 0 + 1 = 1
Value of A So, A = 1 .
Finding B To find the value of B, we substitute x = 2 into the equation y = 2 x + 1 .
Calculating B B = 2 ( 2 ) + 1 = 4 + 1 = 5
Value of B So, B = 5 .
Final Answer Therefore, the values that should replace A and B are 1 and 5, respectively.
Examples
Imagine you're tracking the growth of a plant. Each week, the plant grows twice as much as the previous week, plus an extra inch. The equation y = 2 x + 1 models this growth, where x is the number of weeks and y is the height of the plant. Filling out the table helps you predict the plant's height at different weeks. This kind of linear relationship is useful in many real-world scenarios, from calculating costs to predicting outcomes based on a consistent rate of change.
A = 1 and B = 5 are the values that complete the table for the equation y = 2x + 1. By substituting the respective x values into the equation, we can determine these missing values. This method demonstrates how linear equations relate x and y values consistently.
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