https://file.aiquickdraw.com/mathbot/file/1727195913333ggniibi3.jpg

Let's analyze the graph to answer both parts of the question:

### a) **What is the \( y \)-intercept of this line?**

The \( y \)-intercept is where the line crosses the \( y \)-axis. From the graph, we can observe that the line crosses the \( y \)-axis at \( y = 5 \). So, the \( y \)-intercept is:

\[
y = 5
\]

### b) **What is the gradient (slope) of this line?**

The gradient (slope) of a line is calculated by the formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{change in } y}{\text{change in } x}
\]

From the graph, we can select two points on the line to calculate the slope. Let’s use the points:
- \( (0, 5) \) (the \( y \)-intercept)
- \( (-5, 0) \) (where the line crosses the \( x \)-axis)

The change in \( y \) is from 5 to 0, so \( \Delta y = 5 - 0 = 5 \).

The change in \( x \) is from 0 to -5, so \( \Delta x = 0 - (-5) = 5 \).

Thus, the gradient is:

\[
\text{slope} = \frac{5}{5} = 1
\]

### Final Answers:
- \( y \)-intercept: \( y = 5 \)
- Gradient: \( 1 \)

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Do you want more details or have any questions?

Here are some related questions:
1. What is the general form of a linear equation?
2. How can you calculate the slope if the points are not given clearly?
3. What happens if the gradient of a line is negative?
4. How does the slope affect the angle of the line with respect to the \( x \)-axis?
5. How can we verify the \( y \)-intercept using the equation of the line?

**Tip:** The gradient tells you how steep a line is. A larger gradient means a steeper line!

A straight line is shown on the coordinate grid. What is the y-intercept of the line, and what is the gradient of the line?

Analyze the straight line on the coordinate grid to determine the y-intercept and gradient. This problem involves key concepts of coordinate geometry and the slope-intercept form of linear equations. Suitable for students in Grades 8-10.

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