To find the gradient and $y$-intercept of the line on the graph, let's analyze the graph step-by-step.

Step 1: Determine the Gradient (Slope)

The gradient of a line is calculated using the formula: $\text{Gradient} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ Looking at the graph, let's pick two points on the line:

• Point 1: (0, 10) — This is the $y$-intercept where the line crosses the $y$-axis.
• Point 2: (20, 60)

Using these points: $\text{Gradient} = \frac{60 - 10}{20 - 0} = \frac{50}{20} = 2.5$

Step 2: Determine the $y$-Intercept

The $y$-intercept is the value where the line crosses the $y$-axis. From the graph, this occurs at $y = 10$.

Final Answer

• Gradient: $2.5$
• $y$-Intercept: $10$

Would you like further details or have any questions?

Related Questions

1. How can we verify the gradient using different points on the line?
2. What is the significance of the $y$-intercept in this context?
3. How would the line change if the gradient were negative?
4. What does the gradient tell us about the steepness of the line?
5. How would you plot a line with a gradient of 1.5 and a $y$-intercept of 5?

Tip

For accurate gradient calculations, always pick points that align with the grid intersections to avoid estimation errors.