Question

Create a linear model for the data in the table.
x
4
6
8
10
12
14

y
7
14
21
28
36
45
Question content area bottom
Part 1
Write a linear model for the data in the table.
yequals
  
enter your response herexplus​(
  
enter your response here​)
​(Type integers or decimals rounded to three decimal places as​ needed.)

Answer 1

To create a linear model from the data provided in the table, we need to find the linear relationship between \(x\) and \(y\). The form of a linear equation is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

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

To find the slope, we can use the formula:

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

We can calculate \(m\) using any two points. Let's choose the first two points where \( (x_1, y_1) = (4, 7) \) and \( (x_2, y_2) = (6, 14) \):

\[
m = \frac{(14 - 7)}{(6 - 4)} = \frac{7}{2} = 3.5
\]

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

Next, we can use one of the points and the slope to find the y-intercept \(b\). Using the point \( (4, 7) \):

\[
y = mx + b
\]

Substituting known values:

\[
7 = 3.5(4) + b
\]

Calculating \(3.5(4)\):

\[
7 = 14 + b
\]

Rearranging to find \(b\):

\[
b = 7 - 14 = -7
\]

### Final Model

Now, we can write the linear model:

\[
y = 3.5x - 7
\]

Thus, the final answer for your linear model is:

\[
y = 3.5x + (-7)
\]

So to input this into your specified format:

\[
y = 3.5 x + (-7)
\]

Here’s a recap:

- \(m = 3.5\)
- \(b = -7\)

You should enter:

- \(m = 3.5\)
- \(b = -7\)