Question

A coordinate plane with four quadrants shows the x-axis ranging from negative 7 to 4 in increments of 1, and the y-axis ranging from negative 9 to 8 in increments of 1. An upward line with arrows at both the ends is shown on the plane. The line passes through the first, second, and third quadrants. The line intersects the x-axis at left parenthesis negative 1.5 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis. "/>Use the image to answer the question. Sekou sketched the graph shown based on a verbal description. Fill in the blanks to tell what information she was likely given. (1 point) The initial value of the function is . The function has a constant rate of change equal to .

Answer 1

To determine the initial value of the function and the rate of change based on the description of the line provided, we can use the intercepts:

1. **Initial Value**: The initial value of the function, also known as the y-intercept, is the point where the line intersects the y-axis. From the given information, the line intersects the y-axis at \( (0, 3) \). Therefore, the initial value of the function is **3**.

2. **Rate of Change**: The rate of change of the function can be derived from the slope of the line. The slope (m) can be calculated using the two points where the line intersects the axes:

- The x-intercept is \( (-1.5, 0) \)
- The y-intercept is \( (0, 3) \)

Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

- Let \( (x_1, y_1) = (-1.5, 0) \) and \( (x_2, y_2) = (0, 3) \).

So, we have:

\[
m = \frac{3 - 0}{0 - (-1.5)} = \frac{3}{1.5} = 2
\]

Thus, the function has a constant rate of change equal to **2**.

Putting it all together, the filled-in blanks would be:

- The initial value of the function is **3**.
- The function has a constant rate of change equal to **2**.