Question
The table shows some of the ordered pairs for linear function M.
The equation for linear function N is y=-1/2x+2
.
Which of the following statements is true?
The rate of change for function M is less than the rate of change for function N.
The rate of change for function M is equal to the rate of change for function N.
The initial value of function M is less than the initial value of function N.
The initial value of function M is equal to the initial value of function N.
The equation for linear function N is y=-1/2x+2
.
Which of the following statements is true?
The rate of change for function M is less than the rate of change for function N.
The rate of change for function M is equal to the rate of change for function N.
The initial value of function M is less than the initial value of function N.
The initial value of function M is equal to the initial value of function N.
Answers
GPT-4o mini
To compare the rates of change and initial values (y-intercepts) of the linear functions M and N, let’s analyze the given function N, which is defined by the equation:
\[ y = -\frac{1}{2}x + 2 \]
1. **Rate of Change**: The rate of change (slope) of function N is the coefficient of x in the equation, which is \(-\frac{1}{2}\).
2. **Initial Value**: The initial value (y-intercept) of function N is the constant term in the equation, which is 2.
Now, regarding function M, without specific ordered pairs provided in your message, we can't directly compare its rate of change or initial value to function N.
However, we can analyze the truth of the statements based on some hypothesized properties:
- **Rate of Change for Function M**: If the slope of function M (let's denote it as \(m_{M}\)) is less than \(-\frac{1}{2}\), then the first statement is true. If \(m_{M}\) is greater than \(-\frac{1}{2}\), then the first statement would be false.
- **Initial Value of Function M**: Likewise, if the y-intercept of function M (let's denote it as \(b_{M}\)) is less than 2, then the third statement is true. If \(b_{M}\) equals 2, then the fourth statement would be true.
To firmly establish which statement is true, you need to evaluate the specific ordered pairs of function M. If function M's slope and y-intercept are known, you can draw conclusions about the statements in question.
Please provide the ordered pairs for function M to provide a specific answer.
\[ y = -\frac{1}{2}x + 2 \]
1. **Rate of Change**: The rate of change (slope) of function N is the coefficient of x in the equation, which is \(-\frac{1}{2}\).
2. **Initial Value**: The initial value (y-intercept) of function N is the constant term in the equation, which is 2.
Now, regarding function M, without specific ordered pairs provided in your message, we can't directly compare its rate of change or initial value to function N.
However, we can analyze the truth of the statements based on some hypothesized properties:
- **Rate of Change for Function M**: If the slope of function M (let's denote it as \(m_{M}\)) is less than \(-\frac{1}{2}\), then the first statement is true. If \(m_{M}\) is greater than \(-\frac{1}{2}\), then the first statement would be false.
- **Initial Value of Function M**: Likewise, if the y-intercept of function M (let's denote it as \(b_{M}\)) is less than 2, then the third statement is true. If \(b_{M}\) equals 2, then the fourth statement would be true.
To firmly establish which statement is true, you need to evaluate the specific ordered pairs of function M. If function M's slope and y-intercept are known, you can draw conclusions about the statements in question.
Please provide the ordered pairs for function M to provide a specific answer.