Question
The graph of a linear function is shown on the grid.
What is the rate of change of y
with respect to x
for this function?
What is the rate of change of y
with respect to x
for this function?
Answers
GPT-4o mini
To determine the rate of change of \( y \) with respect to \( x \) for a linear function, we need to find the slope of the line represented by the graph. The slope (rate of change) is calculated using the formula:
\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]
Where \( \Delta y \) is the change in the \( y \)-values and \( \Delta x \) is the change in the \( x \)-values between two points on the line.
1. Identify two distinct points on the line. Let's say these points are \( (x_1, y_1) \) and \( (x_2, y_2) \).
2. Calculate \( \Delta y = y_2 - y_1 \).
3. Calculate \( \Delta x = x_2 - x_1 \).
4. Substitute these values into the slope formula to find the rate of change.
Once you have the slope calculated, that value represents the rate of change of \( y \) with respect to \( x \) for the given linear function. If you can provide specific points from the graph, I can help you calculate the exact slope!
\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]
Where \( \Delta y \) is the change in the \( y \)-values and \( \Delta x \) is the change in the \( x \)-values between two points on the line.
1. Identify two distinct points on the line. Let's say these points are \( (x_1, y_1) \) and \( (x_2, y_2) \).
2. Calculate \( \Delta y = y_2 - y_1 \).
3. Calculate \( \Delta x = x_2 - x_1 \).
4. Substitute these values into the slope formula to find the rate of change.
Once you have the slope calculated, that value represents the rate of change of \( y \) with respect to \( x \) for the given linear function. If you can provide specific points from the graph, I can help you calculate the exact slope!