https://file.aiquickdraw.com/mathbot/file/1729529244935ijzvhnr3.jpg

Let's work out the gradient and the \( y \)-intercept of the line based on the graph.

### Step 1: Determine the Gradient
The gradient \( m \) of a line is calculated using the formula:
\[
m = \frac{{\Delta y}}{{\Delta x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]
From the graph:
- Take two clear points on the line. Let's use \( (0, 10) \) and \( (10, 40) \).
- Applying these coordinates to the formula:
\[
m = \frac{{40 - 10}}{{10 - 0}} = \frac{{30}}{{10}} = 3
\]
So, the gradient \( m = 3 \).

### Step 2: Find the \( y \)-Intercept
The \( y \)-intercept is the point where the line crosses the \( y \)-axis. From the graph, the line crosses the \( y \)-axis at \( y = 10 \).

### Final Answer:
- Gradient: \( 3 \)
- \( y \)-Intercept: \( 10 \)

Would you like more details, or do you have any questions?

Here are 5 related questions to practice:
1. How would the line look if the gradient was negative?
2. What is the equation of the line based on the gradient and \( y \)-intercept found?
3. How do you find the gradient if the line is vertical or horizontal?
4. What happens to the \( y \)-intercept if the line shifts upwards?
5. How would you calculate the gradient if the points were decimals?

**Tip:** When reading values off a graph, always pick points that clearly lie on grid intersections for accuracy.

Work out the gradient and the y-intercept of the line on the graph below.

Learn how to find the gradient and y-intercept of a line from a graph. This problem involves using the gradient formula and identifying the y-intercept visually. Suitable for students in Grades 7-9.

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