Cynthia has measured the weight and miles per gallon of four different cars, listed the data in a table, and graphed the results on a scatterplot. She noticed the points fall closely on a line.

Weight, in hundreds of pounds	Miles per Gallon (mpg)
5	32
10	27
12	25
15	22

Using the data values that Cynthia collected, select the correct slope and y-intercept.


A.)
s l o p e equals short dash 1 semicolon
y minus i n t e r c e p t equals 0


B.)
s l o p e equals short dash 1 semicolon
y minus i n t e r c e p t equals 37


C.)
s l o p e equals 1 semicolon 
y minus i n t e r c e p t equals 27


D.)
s l o p e equals 1 semicolon
y minus i n t e r c e p t equals short dash 27

To solve this problem, we can determine the slope and y-intercept of the line formed by the data points. The equation of a line is given by:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. Let's follow these steps:

### Step 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 choose any two points from the table to calculate the slope. Let's pick the first two points:
- Point 1: (5, 32)
- Point 2: (10, 27)

Now, calculate the slope:

\[
m = \frac{27 - 32}{10 - 5} = \frac{-5}{5} = -1
\]

So, the slope \( m \) is \( -1 \).

### Step 2: Find the y-intercept \( b \)
To find the y-intercept, we can use the slope-intercept form of the line \( y = mx + b \). We already know the slope \( m = -1 \), so we substitute a point from the table to find \( b \).

Using Point 1: (5, 32):

\[
32 = (-1)(5) + b
\]
\[
32 = -5 + b
\]
\[
b = 32 + 5 = 37
\]

So, the y-intercept \( b \) is 37.

### Step 3: Select the correct option
From the calculations, the slope is \( -1 \) and the y-intercept is 37. The correct choice is:

\[
\boxed{B. \text{slope} = -1, \text{y-intercept} = 37}
\]

Let me know if you want any further explanation or have more questions!

Here are 5 relative questions:
1. How does changing the slope affect the steepness of the line?
2. How would the line look if the y-intercept were negative?
3. Can you explain what the y-intercept represents in a real-world context?
4. How do you interpret the meaning of the slope in this scenario?
5. What happens to the line if the weight increases beyond 15?

**Tip**: Always double-check your slope by using different pairs of points to ensure accuracy!

Cynthia has measured the weight and miles per gallon of four different cars, listed the data in a table, and graphed the results on a scatterplot. She noticed the points fall closely on a line.

Weight, in hundreds of pounds  Miles per Gallon (mpg)
5  32
10  27
12  25
15  22

Using the data values that Cynthia collected, select the correct slope and y-intercept.

Learn how to calculate the slope and y-intercept from a table showing car weights and miles per gallon data. This problem demonstrates the use of the slope formula and the equation of a line, suitable for students in Grades 8-10. Discover the relationship between weight and fuel efficiency through a scatterplot analysis.

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