Slope in Geometry Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Find the slope of the line through

A(-2, 5)

and

B(4, -1)

. Describe what the slope tells us about the line's direction.

Solution

1
Step 1: Apply the slope formula: $m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-1 - 5}{4 - (-2)} = \dfrac{-6}{6} = -1$ .
2
Step 2: A slope of $-1$ means the line falls $1$ unit for every $1$ unit moved to the right.
3
Step 3: The line makes a $45°$ angle below horizontal (since $|m|=1$ and the slope is negative, it descends left-to-right).

Answer

m = -1

; the line descends at

45°

from left to right.

Slope measures steepness and direction: positive slope rises left-to-right, negative slope falls, zero is horizontal, undefined is vertical. A slope of