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.

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.

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

The data can be represented as follows:

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

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

Final Answer