In the xy-plane, line k passes through the points (2, 5) and (6, 13). What is the slope of… — GRE General Test

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

The slope of line

k

2

The slope of a straight line passing through points

(x_1, y_1)

and

(x_2, y_2)

is calculated as

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

. Substituting

(2, 5)

and

(6, 13)

gives

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

Identify the given points on the line.

(x_1, y_1) = (2, 5)

and

(x_2, y_2) = (6, 13)

These coordinates provide the required values for the slope formula.

Apply the slope formula

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

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

The slope is defined as the change in vertical position (

y

) divided by the change in horizontal position (

x

Simplify the fraction.

m = 2

Dividing

8

4

yields the simplified slope of the line.

Slope of a Line in Coordinate Geometry

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