Question
The table shows some of the ordered pairs for linear function M.
The equation for linear function N is y=-3/2x+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=-3/2x+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 determine which statement is true regarding the linear functions M and N, we first need to analyze the properties of the linear function N.
The given equation for function N is:
\[ y = -\frac{3}{2}x + 2 \]
From this equation, we can identify the following:
1. **Rate of Change (Slope):** The coefficient of \(x\) in the equation \(y = mx + b\) represents the rate of change (or slope) of the function. For function N, the rate of change is \(-\frac{3}{2}\).
2. **Initial Value (y-intercept):** The constant term in the equation, which is \(b\) in the slope-intercept form, indicates the initial value (the value of \(y\) when \(x = 0\)). For function N, the initial value is \(2\).
Next, we need to compare these properties with those of function M:
- If we had access to the values of function M (the ordered pairs), we could determine its rate of change and initial value.
- Without specific values from function M, we can only evaluate the statements based on assumptions.
However, let's analyze the statements:
1. **"The rate of change for function M is less than the rate of change for function N."** - This is a comparison between the slopes.
2. **"The rate of change for function M is equal to the rate of change for function N."** - If the slopes are equal, this would be true.
3. **"The initial value of function M is less than the initial value of function N."** - This compares the y-intercepts.
4. **"The initial value of function M is equal to the initial value of function N."** - If the y-intercepts are equal, this would be true.
To conclude, since I do not have specific data about function M to make precise comparisons, I can't definitively determine which statement is true. If you provide the specific ordered pairs for function M, I can help analyze the statements directly based on those values. Otherwise, resolving the statements requires knowledge of the slopes and intercepts from function M.
The given equation for function N is:
\[ y = -\frac{3}{2}x + 2 \]
From this equation, we can identify the following:
1. **Rate of Change (Slope):** The coefficient of \(x\) in the equation \(y = mx + b\) represents the rate of change (or slope) of the function. For function N, the rate of change is \(-\frac{3}{2}\).
2. **Initial Value (y-intercept):** The constant term in the equation, which is \(b\) in the slope-intercept form, indicates the initial value (the value of \(y\) when \(x = 0\)). For function N, the initial value is \(2\).
Next, we need to compare these properties with those of function M:
- If we had access to the values of function M (the ordered pairs), we could determine its rate of change and initial value.
- Without specific values from function M, we can only evaluate the statements based on assumptions.
However, let's analyze the statements:
1. **"The rate of change for function M is less than the rate of change for function N."** - This is a comparison between the slopes.
2. **"The rate of change for function M is equal to the rate of change for function N."** - If the slopes are equal, this would be true.
3. **"The initial value of function M is less than the initial value of function N."** - This compares the y-intercepts.
4. **"The initial value of function M is equal to the initial value of function N."** - If the y-intercepts are equal, this would be true.
To conclude, since I do not have specific data about function M to make precise comparisons, I can't definitively determine which statement is true. If you provide the specific ordered pairs for function M, I can help analyze the statements directly based on those values. Otherwise, resolving the statements requires knowledge of the slopes and intercepts from function M.