To find the gradients of lines $A$ and $B$ from the graph:

Formula for Gradient

The gradient (slope) of a straight line is given by: $m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in } y}{\text{Change in } x}$ where $\Delta y$ is the vertical change and $\Delta x$ is the horizontal change between two points on the line.

Step 1: Line $A$ (Blue Line)

1. Identify two clear points on line $A$:
   From the graph, points are approximately $(2, -2)$ and $(3, 6)$.
2. Calculate $\Delta y$ and $\Delta x$:
   $\Delta y = 6 - (-2) = 8, \quad \Delta x = 3 - 2 = 1$
3. Compute the gradient:
   $m_A = \frac{\Delta y}{\Delta x} = \frac{8}{1} = 8$

Gradient of $A$ is 8.

Step 2: Line $B$ (Green Line)

1. Identify two clear points on line $B$:
   From the graph, points are approximately $(0, 12)$ and $(2, 4)$.
2. Calculate $\Delta y$ and $\Delta x$:
   $\Delta y = 4 - 12 = -8, \quad \Delta x = 2 - 0 = 2$
3. Compute the gradient:
   $m_B = \frac{\Delta y}{\Delta x} = \frac{-8}{2} = -4$

Gradient of $B$ is -4.

Final Answer:

• Gradient of $A$: $m_A = 8$
• Gradient of $B$: $m_B = -4$

Let me know if you'd like detailed clarifications or further steps!

Related Questions:

1. How do you interpret positive and negative gradients on a graph?
2. Can you calculate the equation of each line using the gradients found?
3. What is the y-intercept of line $A$? How is it determined from the graph?
4. How does the steepness of a line relate to its gradient value?
5. Can we find the point of intersection of $A$ and $B$ from the graph?

Tip:

To avoid errors when finding gradients, always use exact points (like where lines cross grid intersections) for calculating $\Delta y$ and $\Delta x$.