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.
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.
Solution
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-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.
Step 2: Representing the Data
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}
Step 3: Graphical Representation
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.