https://file.aiquickdraw.com/mathbot/file/1729538289262n8sr6c0s.jpg

The graph shows the equation representing **Relationship A**. We can calculate the slope (rate of change) for Relationship A by using the two points given on the line: \((4, 2)\) and \((8, 4)\).

The slope \( m \) is calculated as:

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

Using the points:

\[
m = \frac{4 - 2}{8 - 4} = \frac{2}{4} = \frac{1}{2}
\]

Thus, the equation for **Relationship A** is:

\[
y = \frac{1}{2}x
\]

Since the question states that **Relationship B** has a greater rate (slope) than **Relationship A**, we are looking for equations where the slope is greater than \( \frac{1}{2} \).

Let's analyze the given options:

1. \( y = \frac{3}{4}x \) → Slope = \( \frac{3}{4} \), which is greater than \( \frac{1}{2} \).
2. \( y = \frac{2}{3}x \) → Slope = \( \frac{2}{3} \), which is greater than \( \frac{1}{2} \).
3. \( y = \frac{1}{4}x \) → Slope = \( \frac{1}{4} \), which is **less** than \( \frac{1}{2} \).
4. \( y = 0.6x \) → Slope = \( 0.6 = \frac{6}{10} = \frac{3}{5} \), which is greater than \( \frac{1}{2} \).

### Correct answers:
- \( y = \frac{3}{4}x \)
- \( y = \frac{2}{3}x \)
- \( y = 0.6x \)

Would you like further details on how to interpret the slope and its impact on graph steepness?

Here are 5 related questions:
1. How do you calculate the slope of a line given two points?
2. What does the slope represent in a linear equation?
3. How does the steepness of the line relate to the slope?
4. Can you explain the difference between positive and negative slopes?
5. How would a vertical or horizontal line's equation differ in terms of slope?

**Tip:** In a linear equation \( y = mx + b \), the slope \( m \) determines the steepness of the line, while \( b \) (the y-intercept) determines where the line crosses the y-axis.

Relationship B has a greater rate than Relationship A. This graph represents Relationship A. Which equations could represent Relationship B? (Select each correct answer)

Analyze linear equations by comparing slopes to determine which one has a greater rate. Using the graph provided for Relationship A, this problem covers key concepts like the slope formula and linear equations. Suitable for Grades 7-9.

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