Questions: Consider a diagram in which the variable measured on the y-axis remains constant while the variable measured on the x-axis increases. The graph of these two variables is a horizontal line, a vertical line, a line that has a negative slope, non-existent because the two variables are not related, or a line that has positive slope.

Consider a diagram in which the variable measured on the y-axis remains constant while the variable measured on the x-axis increases. The graph of these two variables is a horizontal line, a vertical line, a line that has a negative slope, non-existent because the two variables are not related, or a line that has positive slope.
Transcript text: Consider a diagram in which the variable measured on the $y$-axis remains constant while the variable measured on the $x$-axis increases. The graph of these two variables is a horizontal line. a vertical line. a line that has a negative slope. non-existent because the two variables are not related. a line that has positive slope.
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Solution

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Solution Steps

To determine the type of graph described, we need to understand the relationship between the variables on the x-axis and y-axis. If the variable on the y-axis remains constant while the variable on the x-axis increases, the graph will be a horizontal line.

Step 1: Understanding the Relationship Between Variables

Given that the variable measured on the y y -axis remains constant while the variable measured on the x x -axis increases, we can infer that the graph will be a horizontal line. This is because the y y -value does not change as the x x -value increases.

Step 2: Representing the Data

The data can be represented as follows:

  • x x values: x={0,1,2,3,4,5,6,7,8,9} x = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}
  • y y values: y={5,5,5,5,5,5,5,5,5,5} y = \{5, 5, 5, 5, 5, 5, 5, 5, 5, 5\}
Step 3: Graphical Representation

The graphical representation of the data shows a horizontal line at y=5 y = 5 . This confirms that the y y -value remains constant while the x x -value increases.

Final Answer

a horizontal line\boxed{\text{a horizontal line}}

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