Find the gradients of the line joining the following pairs of points: a) (2,5) and (4,8) b) (-3,2) and (4,4)

Mathematics
Find the gradients of the line joining the following pairs of points: a) (2,5) and (4,8) b) (-3,2) and (4,4)

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Answer

2

Part (b)

Step 1: The formula for the gradient mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Step 2: The points are (x1,y1)=(2,3)(x_1, y_1) = (2, 3) and (x2,y2)=(4,7)(x_2, y_2) = (4, 7).

Substitute the values:

m=7−34−2m = \frac{7 - 3}{4 - 2}

Step 3: Simplify:

m=42=2m = \frac{4}{2} = 2

The gradient is 2\boxed{2}.

Part (c)

Step 1: The formula for the gradient mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Step 2: The points are (x1,y1)=(3,5)(x_1, y_1) = (3, 5) and (x2,y2)=(6,11)(x_2, y_2) = (6, 11).

Substitute the values:

m=11−56−3m = \frac{11 - 5}{6 - 3}

Step 3: Simplify:

m=63=2m = \frac{6}{3} = 2

The gradient is 2\boxed{2}.

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Part (b) Step 1: The formula for the gradient m of a line passing through two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1) Step 2: The points are (x_1, y_1) = (2, 3) and (x_2, y_2) = (4, 7).

Find the gradients of the line joining the following pairs of points: a) (2,5) and (4,8) b) (-3,2) and (4,4)
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 (b) Step 1: The formula for the gradient m of a line passing through two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1) Step 2: The points are (x_1, y_1) = (2, 3) and (x_2, y_2) = (4, 7). Substitute the values: m = (7 - 3)/(4 - 2) Step 3: Simplify: m = (4)/(2) = 2 The gradient is 2. Part (c) Step 1: The formula for the gradient m of a line passing through two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1) Step 2: The points are (x_1, y_1) = (3, 5) and (x_2, y_2) = (6, 11). Substitute the values: m = (11 - 5)/(6 - 3) Step 3: Simplify: m = (6)/(3) = 2 The gradient is 2.