P is a linear function represented by the equation

Question

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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.