The diagram shows two parallel lines. a) Work out the gradient of line A. b) Write down the gradient of line B.

Mathematics
The diagram shows two parallel lines. a) Work out the gradient of line A. b) Write down the gradient of line B.

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Answer

2

Part (a)

Step 1: The gradient mm of a straight line is calculated using the formula

m=y2−y1x2−x1.m = \frac{y_2 - y_1}{x_2 - x_1}.

Step 2: From the diagram, two points on line A are (1,2)(1,2) and (2,4)(2,4).

Step 3: Substitute the coordinates into the formula:

mA=4−22−1=21=2.m_A = \frac{4 - 2}{2 - 1} = \frac{2}{1} = 2.

The gradient of line A is 2\mathbf{2}.

Part (b)

Step 1: The diagram shows two parallel lines.

Step 2: Parallel lines have equal gradients.

Step 3: Therefore, the gradient of line B is the same as the gradient of line A, which is 2\mathbf{2}.

2

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Part (a) Step 1: The gradient m of a straight line is calculated using the formula m = (y_2 - y_1)/(x_2 - x_1).

The diagram shows two parallel lines. a) Work out the gradient of line A. b) Write down the gradient of line B.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Part (a) Step 1: The gradient m of a straight line is calculated using the formula m = (y_2 - y_1)/(x_2 - x_1). Step 2: From the diagram, two points on line A are (1,2) and (2,4). Step 3: Substitute the coordinates into the formula: m_A = (4 - 2)/(2 - 1) = (2)/(1) = 2. The gradient of line A is 2. Part (b) Step 1: The diagram shows two parallel lines. Step 2: Parallel lines have equal gradients. Step 3: Therefore, the gradient of line B is the same as the gradient of line A, which is 2. 2