Subjects algebra

Line Gradient Ae4Ad4

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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