Question

Use the table to answer the question. x y 1 4 −3 8 Find the rate of change and the initial value of the linear function given as a table of values. (1 point) The rate of change is m= , and the initial value is b= . Remaining Attempts : 3

Answer 1

To find the rate of change and the initial value of the linear function from the table, we can follow these steps:

1. **Identify the points from the table**:
Given the values:
- (1, 4)
- (-3, 8)

2. **Calculate the rate of change (slope)**:
The slope \( m \) is calculated using the formula:

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

Let's assign the points:
- \( (x_1, y_1) = (1, 4) \)
- \( (x_2, y_2) = (-3, 8) \)

Plugging in the values:

\[
m = \frac{8 - 4}{-3 - 1} = \frac{4}{-4} = -1
\]

3. **Identify the initial value (y-intercept)**:
The initial value \( b \) (y-intercept) can be found using one of the points and the slope in the slope-intercept form of a linear equation \( y = mx + b \).

Using point \( (1, 4) \) and plugging into the equation:

\[
4 = -1(1) + b
\]

\[
4 = -1 + b \rightarrow b = 4 + 1 \rightarrow b = 5
\]

Now we have the rate of change and the initial value:

- The rate of change \( m = -1 \)
- The initial value \( b = 5 \)

**Final answer**: The rate of change is \( m = -1 \), and the initial value is \( b = 5 \).