Math  /  Algebra

QuestionA line passes through the points (1,2)(1,2) and (5,10)(5,10). Find its gradient.

Studdy Solution

STEP 1

1. The gradient (or slope) of a line passing through two points can be found using the formula: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} .
2. The points given are (1,2) (1, 2) and (5,10) (5, 10) .
3. The coordinates of the points are (x1,y1)=(1,2) (x_1, y_1) = (1, 2) and (x2,y2)=(5,10) (x_2, y_2) = (5, 10) .

STEP 2

1. Identify the coordinates of the two points.
2. Substitute the coordinates into the gradient formula.
3. Simplify the expression to find the gradient.

STEP 3

Identify the coordinates of the two points: (x1,y1)=(1,2) (x_1, y_1) = (1, 2) (x2,y2)=(5,10) (x_2, y_2) = (5, 10)

STEP 4

Substitute the coordinates into the gradient formula: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} m=10251 m = \frac{10 - 2}{5 - 1}

STEP 5

Simplify the expression to find the gradient: m=84 m = \frac{8}{4} m=2 m = 2
The gradient of the line passing through the points (1,2) (1, 2) and (5,10) (5, 10) is 2 2 .

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