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.