Select all the correct answers.
Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.



x	y
7	8
14	16
21	24
 line 1
 line 2
 line 3
 line 4
 line 5

To solve this problem, we need to calculate the unit rate of the relationship in the table and compare it to the unit rates of the lines on the graph. The unit rate refers to the slope of a line (the change in \( y \) divided by the change in \( x \)).

### Step 1: Find the unit rate from the table
The data in the table shows a linear relationship between \( x \) and \( y \). To find the unit rate (slope), we calculate the change in \( y \) divided by the change in \( x \).

Looking at the table, we can see that:
- When \( x = 7 \), \( y = 8 \)
- When \( x = 14 \), \( y = 16 \)
- When \( x = 21 \), \( y = 24 \)

The slope (unit rate) is calculated as:
\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{16 - 8}{14 - 7} = \frac{8}{7}
\]
So, the unit rate is \( \frac{8}{7} \approx 1.14 \).

### Step 2: Compare with the lines on the graph
Now we need to check which lines on the graph have unit rates that are:
- Greater than \( 1.14 \) (the unit rate from the table).
- Less than 2.

Since we do not have the explicit equations of the lines, you can calculate the slopes of the lines on the graph by picking two points for each line and applying the same formula for slope:
\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x}
\]
Then, select the lines whose slopes are greater than 1.14 but less than 2.

If you have specific data points for the lines or a graph available, feel free to share them so we can proceed with calculating their slopes.

Would you like more details on how to calculate the slopes of each line? Also, here are some follow-up questions:

1. How do you interpret a unit rate in the context of a linear relationship?
2. What is the significance of comparing unit rates between different lines?
3. How can you determine if a relationship is proportional by looking at a graph?
4. What would a unit rate of 1 indicate about the relationship between \( x \) and \( y \)?
5. How do changes in the slope affect the steepness of a line on the graph?

**Tip:** Always use two distinct points on a line to accurately calculate the slope.

Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.

Learn how to find lines on a graph with unit rates between specific values by comparing them to the unit rate calculated from a given table. Understand concepts like slope, linear relationships, and unit rates with practical examples. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation