Fill in the table using the equation y = 2x + 5.
Understand the Problem
The question is asking to fill in a table that relates x values to y values using the equation y = 2x + 5. The goal is to calculate y for corresponding x values and fill in the respective coordinates (x, y) in the table.
Answer
The coordinates in the table are $(0, 5)$, $(1, 7)$, $(2, 9)$, $(3, 11)$.
Answer for screen readers
The table will include the following coordinates:
- $(0, 5)$
- $(1, 7)$
- $(2, 9)$
- $(3, 11)$
Steps to Solve
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Identify the equation The equation given is $y = 2x + 5$. This equation relates the values of $x$ and $y$.
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Select x values Choose some values for $x$ to calculate corresponding $y$ values. For example, let’s use $x = 0$, $x = 1$, $x = 2$, and $x = 3$.
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Calculate y values Using the equation, calculate $y$ for each selected $x$:
- For $x = 0$: $$y = 2(0) + 5 = 5$$
- For $x = 1$: $$y = 2(1) + 5 = 7$$
- For $x = 2$: $$y = 2(2) + 5 = 9$$
- For $x = 3$: $$y = 2(3) + 5 = 11$$
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Fill in the table Record the $x$ and corresponding $y$ values as coordinates $(x, y)$ in the table:
- For $x = 0$: The coordinate is $(0, 5)$.
- For $x = 1$: The coordinate is $(1, 7)$.
- For $x = 2$: The coordinate is $(2, 9)$.
- For $x = 3$: The coordinate is $(3, 11)$.
The table will include the following coordinates:
- $(0, 5)$
- $(1, 7)$
- $(2, 9)$
- $(3, 11)$
More Information
This method shows how a linear equation relates changes in $x$ to changes in $y$. The equation $y = 2x + 5$ indicates that for every unit increase in $x$, $y$ increases by 2 units.
Tips
- Forgetting to add 5 when calculating $y$ values. Always ensure to apply the entire formula correctly.
- Choosing non-integer values for $x$ without understanding their implications. It’s useful to start with integers first to see the pattern.
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