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.)
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.)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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:
- \(m = 3.5\)
- \(b = -7\)
\[
y = mx + b
\]
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:
- \(m = 3.5\)
- \(b = -7\)
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