In the table as x increases by​ 1, the value of y increases by 2. Complete the table. Describe the relationship between x and y. Then use the table to graph the relationship.

Question

x
0
1
2
3
4
5
y
0
2
4
Question content area bottom
Part 1
Complete the table.
x
0
1
2
3
4
5
y
0
2
4
  
6
  
8
  
10
Part 2
The table shows the relationship between x and y. Which statement expresses that​ relationship?

Answer 1

Part 1: Complete the Table

The given table needs to be completed with values of \( y \) corresponding to \( x \):

| x | y | |---|---| | 0 | 0 | | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 | | 5 | 10 |

Part 2: Describe the Relationship

The relationship between \( x \) and \( y \) can be described as a linear relationship where \( y \) increases by 2 for every increase of 1 in \( x \).

This can be expressed as:

• Statement: "As \( x \) increases by 1, \( y \) increases by 2."

This indicates a direct proportionality where the relationship can be written in the form of a linear equation:

\[ y = 2x \]

Part 3: Graph the Relationship

To graph the relationship represented in the table:

1. Plot the points (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) on a Cartesian plane.
2. Connect the points to form a straight line.

The graph will show a straight line that passes through the origin (0,0) and has a slope of 2, indicating the increasing nature of \( y \) as \( x \) increases.

The line will rise steeply since for every step along the \( x \)-axis (to the right), the line goes up by 2 units along the \( y \)-axis.