Vocabulary

Slope – describes the steepness of a line. It is the ratio of the rise divided by the run.

Rise – It is the vertical change between two points. It is calculated by subtracting the y-coordinates of the points. Going up from the left point to the right point indicates a positive rise. Going down from the left point to the right point indicates a negative rise.

Run – It is the horizontal change between two points. It is calculated by subtracting the x-coordinates of the points. Going right from one point to the other indicates a positive run. Going left from one point to the other indicates a negative run.

Concept

Calculate the slope given the coordinates of two points (x₁,y₁),(x₂,y₂)

Rules

1. Choose one point to be point 1 and the other to be point 2.
2. Substitute the y-coordinates into the numerator of the formula m = $\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}$ and the x-coordinates into the denominator.
3. Simplify the fraction if possible.

Example

What is the slope of a line that passes through the points (5,3) and (8,9)?

$3$

$\frac{1}{2}$

-$2$

$2$

Solution

$\mathrm{m}$ = $\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}$ 

$\mathrm{m}$ = $\frac{9-3}{8-5}$ = $\frac{6}{3}$ = $2$

Pre-requisite Skill

Slope (8.3.2)