a) Copy and complete the table below for the graph of y = 2x. b) The lines y = x and y = 2x are shown on the axis below. Write down one similarity and one difference between these... a) Copy and complete the table below for the graph of y = 2x. b) The lines y = x and y = 2x are shown on the axis below. Write down one similarity and one difference between these lines.
Understand the Problem
The question involves completing a table for the linear function y = 2x, which requires calculating values of y for given x values. It also asks to identify one similarity and one difference between the lines y = x and y = 2x, which involves understanding the concepts of linear equations and their graphical representations.
Answer
The completed values are $A = 0$ and $B = 4$.
Answer for screen readers
The completed table is:
| $x$ | $y$ |
|---|---|
| -2 | -4 |
| -1 | -2 |
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
Where $A = 0$ and $B = 4$.
Steps to Solve
- Calculate $y$ when $x = -2$
Using the equation $y = 2x$: $$y = 2(-2) = -4$$
- Calculate $y$ when $x = -1$
Using the equation $y = 2x$: $$y = 2(-1) = -2$$
- Calculate $y$ when $x = 0$
Using the equation $y = 2x$: $$y = 2(0) = 0$$
- Calculate $y$ when $x = 1$
Using the equation $y = 2x$: $$y = 2(1) = 2$$
- Calculate $y$ when $x = 2$
Using the equation $y = 2x$: $$y = 2(2) = 4$$
- Fill in the values in the table
Now, we can complete the table with the calculated values:
- For $x = -2$, $y = -4$
- For $x = -1$, $y = -2$
- For $x = 0$, $y = 0$ (A)
- For $x = 1$, $y = 2$
- For $x = 2$, $y = 4$ (B)
The completed table is:
| $x$ | $y$ |
|---|---|
| -2 | -4 |
| -1 | -2 |
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
Where $A = 0$ and $B = 4$.
More Information
In the function $y = 2x$, the output $y$ doubles for every increase of $1$ in $x$. This is a characteristic of linear functions with a slope of $2$.
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