https://file.aiquickdraw.com/mathbot/file/1725731348342bo2s2kuw.jpg

The image asks for the **ratio** of the change in \( x \) to the change in \( y \) based on the graph. We can identify the changes from the gridlines on the graph.

From the graph:
- The **change in \( x \)** (horizontal distance) is from \( x = 3 \) to \( x = 7 \), so \( \Delta x = 7 - 3 = 4 \).
- The **change in \( y \)** (vertical distance) is from \( y = 0 \) to \( y = 5 \), so \( \Delta y = 5 - 0 = 5 \).

To find the **ratio** of \( \Delta x \) to \( \Delta y \) in the form \( 1 : n \), we calculate:
\[
\text{Ratio} = \frac{\Delta x}{\Delta y} = \frac{4}{5} = 0.8
\]

Thus, the ratio of the change in \( x \) to the change in \( y \) is \( 1 : 0.8 \).

Let me know if you have any questions or if you would like further details.

### Related Questions:
1. What is the slope of the line in the graph?
2. How does the ratio of change in \( x \) to change in \( y \) relate to the slope?
3. How would the ratio change if \( \Delta x \) was 6 and \( \Delta y \) was 8?
4. What would be the equation of the line passing through the origin with this ratio?
5. How can you express the relationship between \( x \) and \( y \) in this graph?

### Tip:
The ratio of changes in \( x \) and \( y \) is closely related to the slope of the line, which is defined as \( \frac{\Delta y}{\Delta x} \).

For the graph below, calculate the ratio of the change in x to the change in y in the form 1 : n. Give any decimals in your answer to 1 d.p.

Learn how to calculate the ratio of the change in x to the change in y from a graph. Using gridlines to find Δx and Δy, and calculating the ratio in the form 1 : n, this problem covers key concepts like ratios and slope for Grades 7-9.

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