Question

P is a linear function represented by the equation
.

Q is another linear function that includes the ordered pairs shown in the table below.



Which of these linear functions has a negative rate of change?
Function P only
Function Q only
both Function P and Function Q
neither Function P nor Function Q

Answer 1

To determine which linear function has a negative rate of change, we need to analyze the slope (rate of change) of both functions, P and Q.

1. **Function P**: Without the specific equation provided, let’s assume it is in the form of \(y = mx + b\), where \(m\) represents the slope. If \(m < 0\), then Function P has a negative rate of change.

2. **Function Q**: To find the rate of change of Function Q using the ordered pairs from the table, we can calculate the slope (rate of change) using the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
By analyzing the provided ordered pairs, if the change in y (rise) is negative while the change in x (run) is positive, then the slope will also be negative, indicating a negative rate of change.

Once both functions are analyzed:

- If only **Function P** has a negative slope, the answer is "Function P only".
- If only **Function Q** has a negative slope, the answer is "Function Q only".
- If both have negative slopes, the answer is "both Function P and Function Q".
- If neither has a negative slope, the answer is "neither Function P nor Function Q".

Without specific numbers from the equation for Function P and the ordered pairs for Function Q, I cannot give the exact answer. Please provide them for more accurate analysis.