Line Gradient Ae4Ad4
1. **State the problem:** We have a straight line drawn on a centimeter grid. Tina assumes the scale is 1 cm = 1 unit and wants to find the gradient of the line.
2. **Formula for gradient:** The gradient $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Identify points on the line:** From the graph description, approximate two points on the line:
- Point 1: $(0,1)$
- Point 2: $(7,5)$
4. **Calculate the gradient using Tina's assumption:**
$$m = \frac{5 - 1}{7 - 0} = \frac{4}{7}$$
5. **Interpretation of part b:** The actual scale is not 1 cm = 1 unit, but Tina assumed it is. Since the scale changes both axes proportionally, the gradient (which is a ratio) remains the same.
6. **Answer to part b:** The correct statement is C: The answer to part a) stays the same.
**Final answers:**
- Gradient is $\frac{4}{7}$
- Correct statement: C