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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.

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 fill in the blanks based on the given information about the line in the coordinate plane, we can analyze the points where the line intersects the axes.

1. The initial value of the function corresponds to the y-intercept of the line. The line intersects the y-axis at the point (0, 3). Therefore, the initial value is:

   The initial value of the function is 3.

2. The constant rate of change (slope) of the function can be calculated using the two points provided: the x-intercept (-1.5, 0) and the y-intercept (0, 3). The slope (m) can be calculated using the formula:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Here, (x1, y1) is the y-intercept (0, 3) and (x2, y2) is the x-intercept (-1.5, 0).

   Plugging in the values:

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

   Therefore, the constant rate of change is:

   The function has a constant rate of change equal to 2.

To summarize:

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