Use the image to answer the question.

Question

Determine the initial value and the rate of change of the linear function as given in the graph.

(1 point)
Responses

The initial value is 16, and the rate of change is 32.
The initial value is Start Fraction 1 over 6 End Fraction , and the rate of change is Start Fraction 3 over 2 End Fraction .

The initial value is −2, and the rate of change is 23.
The initial value is negative 2 , and the rate of change is Start Fraction 2 over 3 End Fraction .

The initial value is 23, and the rate of change is −23.
The initial value is Start Fraction 2 over 3 End Fraction , and the rate of change is negative Start Fraction 2 over 3 End Fraction .

The initial value is −23, and the rate of change is 23.

Answer 1

Without being able to see the image or graph you are referencing, I can guide you on how to determine the initial value and the rate of change for a linear function.

1. Initial Value: This is the y-value when the x-value is 0. Look for the point where the line intersects the y-axis.

2. Rate of Change (Slope): This is calculated by taking two points on the line, \((x_1, y_1)\) and \((x_2, y_2)\), and using the formula: \[ \text{Rate of Change (Slope)} = \frac{y_2 - y_1}{x_2 - x_1} \] This represents how much y changes for a unit change in x.

If you can describe the graph or give specific coordinates from it, I could help you calculate the initial value and the rate of change. Based on the responses provided, you would have to match your findings with one of the options given.