The function with a constant additive rate of change of -1/4 would exhibit a consistent rate of decrease by 1/4 in its output values for every 1 unit increase in its input values.
Let's analyze the options provided:
1. **The straight line on the coordinate plane:**
- To determine if the line has a constant additive rate of change, we need to find its slope. The slope is calculated as the change in \( y \) divided by the change in \( x \). Based on the points given, \((-2, 2)\) and \((2, 1)\):
\[
\text{slope} = \frac{1 - 2}{2 - (-2)} = \frac{-1}{4} = -\frac{1}{4}
\]
- Therefore, this line has a constant rate of change of -1/4, which matches our requirement.
2. **The curved line on the coordinate plane:**
- A curved line does not have a constant additive rate of change. The rate of change varies at different points on the curve. Hence, this option can be discounted.
3. **The table with \( x \) values (20, 21, 22, 23) and \( y \) values (-1, -1.5, -2, -2.5):**
- To identify the rate of change, calculate the differences in consecutive \( y \) values:
\[
\begin{align*}
-1.5 - (-1) &= -0.5 \\
-2 - (-1.5) &= -0.5 \\
-2.5 - (-2) &= -0.5
\end{align*}
\]
- Each change in \( y \) for a 1 unit increase in \( x \) is -0.5, which is not equal to -1/4. So, this option can be discounted.
4. **The table with \( x \) values (-12, -11, -10, -9) and \( y \) values (7, 11, 14, 17):**
- To identify the rate of change, calculate the differences in consecutive \( y \) values:
\[
\begin{align*}
11 - 7 &= 4 \\
14 - 11 &= 3 \\
17 - 14 &= 3
\end{align*}
\]
- Each change in \( y \) is not consistent, and more importantly, it does not match the required -1/4. Thus, this option is not valid.
Therefore, the correct option is **the straight line on the coordinate plane that passes through (–2, 2) and (2, 1)**, which has a constant additive rate of change of –1/4.
Which function has a constant additive rate of change of –1/4?
A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1).
A coordinate plane with a curved line passing through (negative 1, 2), (0, negative 1), the minimum (2, negative 2), and (4, negative 1).
A two column table with five rows. The first column, x, has the entries, 20, 21, 22, 23. The second column, y, has the entries negative 1, negative 1.5, negative 2, negative 2.5.
A two column table with five rows. The first column, x, has the entries, negative 12, negative 11, negative 10, negative 9. The second column, y, has the entries, 7, 11, 14, 17.
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