Question

Difficulty: EasyCoordinate Geometry: Lines, Slopes, and Distance

In the $xy$ -plane, line $l$ passes through the points $(2, 5)$ and $(6, 13)$ . What is the slope of line $l$ ?

Answer: 2

The slope of line

l

is 2.

The slope of a line passing through

(x_1, y_1)

and

(x_2, y_2)

is given by

m = \frac{y_2 - y_1}{x_2 - x_1}

. Substituting

(2, 5)

and

(6, 13)

into the formula gives

m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2

Identify the coordinates of the two given points on line

l

The points are

(x_1, y_1) = (2, 5)

and

(x_2, y_2) = (6, 13)

Two points are required to calculate the slope of a straight line.

Apply the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2

The slope measures the vertical change (rise) divided by the horizontal change (run).

Slope of a line through two points

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