What is the rate of change of y with respect to x?
Understand the Problem
The question is asking for the rate of change of y with respect to x based on the given graph. This likely involves determining the slope of the line represented in the graph.
Answer
1
Answer for screen readers
The rate of change of (y) with respect to (x) is 1.
Steps to Solve
- Identify two points on the line
Select two clear points on the graph to determine the slope. Let's take the points ((0, 0)) and ((3, 3)).
- Calculate the change in y and change in x
Determine the differences in the y and x coordinates between the two points:
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Change in (y): (y_2 - y_1 = 3 - 0 = 3)
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Change in (x): (x_2 - x_1 = 3 - 0 = 3)
- Compute the slope
The slope (rate of change of (y) with respect to (x)) is calculated using the formula:
$$ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{3}{3} = 1 $$
The rate of change of (y) with respect to (x) is 1.
More Information
The slope of a line represents the rate of change. A slope of 1 means that for every unit increase in (x), (y) increases by 1.
Tips
- Confusing the coordinates or not selecting the correct points on the line.
- Failing to calculate the changes in (y) and (x) accurately.
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