Question

Write a linear function for the data in the table.
x
0
1
2
3
4
y
1
negative 0.5
negative 2
negative 3.5
negative 5
Question content area bottom
Part 1
The linear function for the data in the table is
  
enter your response here

Answer 1

To find the linear function that fits the data provided, we can start by looking for the slope \( m \) and the y-intercept \( b \) for the equation of the line in the form \( y = mx + b \).

**Step 1: Calculate the slope (m)**

We can use the formula for the slope:

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

Let's pick two points from the table. For example, we can use points (0, 1) and (1, -0.5).

- \( (x_1, y_1) = (0, 1) \)
- \( (x_2, y_2) = (1, -0.5) \)

Calculating the slope:

\[
m = \frac{-0.5 - 1}{1 - 0} = \frac{-1.5}{1} = -1.5
\]

**Step 2: Find the y-intercept (b)**

Using the slope \( m = -1.5 \), we can use one of the points (0, 1) to find the y-intercept \( b \):

The equation of the line is:

\[
y = mx + b
\]

Substituting \( m \) and the point (0, 1):

\[
1 = -1.5(0) + b \Rightarrow b = 1
\]

**Step 3: Write the linear function**

Now that we have both \( m \) and \( b \), we can write the linear function:

\[
y = -1.5x + 1
\]

**Final Answer:**

The linear function for the data in the table is:

\[
y = -1.5x + 1
\]