Question

Use the graph of a the function to determine the initial value and the rate of change.

-1,-1 and 0,2

(2 pts)
b =

m=


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Answer 1

To determine the initial value and the rate of change from the points given, we can analyze the coordinates. The points you provided are (-1, -1) and (0, 2).

1. **Initial Value (b)**: This refers to the y-intercept of the function, which is the value of \( y \) when \( x = 0 \). From the given points, at \( x = 0 \), \( y = 2 \). Therefore, the initial value is:
\[ b = 2 \]

2. **Rate of Change (m)**: This refers to the slope of the function, which can be calculated using the formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (-1, -1) and (0, 2):
- Let \((x_1, y_1) = (-1, -1)\) and \((x_2, y_2) = (0, 2)\).
\[
m = \frac{2 - (-1)}{0 - (-1)} = \frac{2 + 1}{0 + 1} = \frac{3}{1} = 3
\]

So, we have:

- \( b = 2 \)
- \( m = 3 \)

Thus:
- \( b = 2 \)
- \( m = 3 \)