Create a linear model for the data in the table.

Question

x
4
6
8
10
12
14

y
6
14
20
28
36
45
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Part 1
Write a linear model for the data in the table.
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Answer 1

To create a linear model \( y = mx + b \) for the given data, we first need to determine the slope \( m \) and the y-intercept \( b \).

Here's how we can derive these values:

1. Calculate the slope \( m \): The slope \( m \) is calculated using the formula: \[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \] We can take two points from the data to calculate this. Let's use the first two points: (4, 6) and (6, 14).

   \[ m = \frac{(14 - 6)}{(6 - 4)} = \frac{8}{2} = 4 \]

2. Using the slope to find the y-intercept \( b \): We can use one of the points to find \( b \). Let's use the point (4, 6): \[ y = mx + b \ 6 = 4(4) + b \ 6 = 16 + b \ b = 6 - 16 = -10 \]

Now we have determined \( m = 4 \) and \( b = -10 \).

3. Write the linear model: Therefore, the linear model is: \[ y = 4x - 10 \]

So the final answer is:

\[ y = 4x + (-10) \]

or just:

\[ y = 4x - 10 \]