Which statement correctly compares the function shown on this graph with the function y = 4x + 2?

An image of a graph showing a relation.
 A. 
The function shown on the graph has a greater rate of change, but a lower starting point.
 B. 
The function shown on the graph has a greater rate of change and a higher starting point.
 C. 
The function shown on the graph has a smaller rate of change and a lower starting point.
 D. 
The function shown on the graph has a smaller rate of change, but a higher starting point.
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To compare the function shown on the graph with the given function \( y = 4x + 2 \), we need to focus on two aspects:

1. **Rate of Change (Slope):** The slope of \( y = 4x + 2 \) is \( 4 \), since it's the coefficient of \( x \) in the linear equation. You would need to determine the slope of the function on the graph and compare it with 4. If the graph's line is steeper than \( y = 4x + 2 \), it has a greater rate of change; if it’s less steep, it has a smaller rate of change.

2. **Starting Point (y-intercept):** The starting point (y-intercept) of \( y = 4x + 2 \) is \( 2 \) (the constant term). You can compare this with the y-intercept of the function on the graph. If the graph starts above \( y = 2 \), it has a higher starting point, and if it starts below, it has a lower starting point.

Without seeing the graph, here’s how you can determine the correct statement:
- **If the graph’s slope is less than 4** and its y-intercept is below 2, the correct answer would be **C**.
- **If the graph’s slope is less than 4** but its y-intercept is above 2, the correct answer would be **D**.
- **If the graph’s slope is greater than 4** but its y-intercept is below 2, the correct answer would be **A**.
- **If the graph’s slope is greater than 4** and its y-intercept is above 2, the correct answer would be **B**.

Let me know if you want more details on how to calculate slope or analyze graph characteristics!

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Here are 5 related questions for further exploration:

1. How do you calculate the slope of a line given two points on the graph?
2. What is the significance of the y-intercept in a linear equation?
3. How does the slope affect the steepness of a graph?
4. Can two lines have the same slope but different y-intercepts? What does this imply?
5. How do you determine if two lines are parallel or perpendicular based on their slopes?

**Tip:** When comparing two linear functions, always check the slope first, as it controls how fast the line rises or falls.

Which statement correctly compares the function shown on this graph with the function y = 4x + 2?

Learn how to compare the linear function y = 4x + 2 with a graph of another function by analyzing their slopes and y-intercepts. This problem covers key algebraic concepts, including slope, rate of change, and y-intercept. Suitable for students in Grades 8-10.

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