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.

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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

  1. Calculate $y$ when $x = -2$

Using the equation $y = 2x$: $$y = 2(-2) = -4$$

  1. Calculate $y$ when $x = -1$

Using the equation $y = 2x$: $$y = 2(-1) = -2$$

  1. Calculate $y$ when $x = 0$

Using the equation $y = 2x$: $$y = 2(0) = 0$$

  1. Calculate $y$ when $x = 1$

Using the equation $y = 2x$: $$y = 2(1) = 2$$

  1. Calculate $y$ when $x = 2$

Using the equation $y = 2x$: $$y = 2(2) = 4$$

  1. 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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