Slope Formula

The slope formula allows you to find the slope of a line using two points (x₁, y₁) and (x₂, y₂) on the line.

The slope formula:

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

The slope, which we label m, provides an idea of how steep a line is.

Example 1 :

Find the slope of the line containing the points (-5, 8) and (6, -14).

Step 1:

Assign coordinate values to (x₁, y₁) and (x₂, y₂).

Point 1: (-5, 8) → X₁ = -5, y₁ = 8

Point 2: (6, -14) → X₂ = 6, y₂ = -14

Step 2:

Substitute into formula and simplify.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{(- 14) - (8)}{(6) - (- 5)}$	Substitute x- and y-values into formula.
$m = \frac{- 22}{11}$	-14 - 8 = -22 and 6 - (-5) = 6 + 5 = 11.
m = -2	-22 divided by 11 equals -2.

Answer: The slope of the line is -2.

Example 2:

Find the slope of the line containing the points (-3, -7) and (-9, -10).

Step 1:

Assign coordinate values to (x₁, y₁) and (x₂, y₂)

Point 1: (-3, -7) → X₁ = -3, y₁ = -7

Point 2: (-9, -10) → X₂ = -9, y₂ = -10

Step 2:

Substitute into formula and simplify.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{(- 10) - (- 7)}{(- 9) - (- 3)}$	Substitute x- and y-values into formula.
$m = \frac{- 3}{- 6}$	(-10) - (-7) = -10 + 7 = -3 and (-9) - (-3) = -9 + 3 = -6.
$m = \frac{1}{2}$	-3 divided by -6 equals $m = \frac{1}{2}$ .

Answer: The slope of the line is $m = \frac{1}{2}$ .

Related Links:

<a href="https://www.softschools.com/formulas/math/slope_formula/140/">Slope Formula </a>

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