Slope Formula Practice

For the following problems, you will practice with slope. Each practice problem will require the following three steps.

First, you'll label x₁,y₁ and x₂,y₂ for the ordered pairs.

(x₁, y₁)	(x₂, y₂)
(3,5)	(7,9)

Then, you'll substitute the values into the formula,

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

$\mathsf{ m = \frac{9 - 5}{7 - 3} }$

Finally, subtract and simplify.

$\mathsf{ m = \frac{9 - 5}{7 - 3} = \frac{4}{4} = 1 }$

Now calculate the slope using the two ordered pairs shown.

(9,3) (14,13)

x₁, y₁	x₂, y₂
(9,3)	(14,13)

$\mathsf{ m = \frac{13-3}{14-9} }$

$\mathsf{ m = \frac{10}{5} = 2 }$

(-4,6) (16,66)

x₁, y₁	x₂, y₂
(-4,6)	(16,66)

$\mathsf{ m = \frac{66-6}{16-(-4)} }$

$\mathsf{ m = \frac{60}{20} = 3 }$

(-5,-8) (2,13)

x₁, y₁	x₂, y₂
(-5,-8)	(2,13)

$\mathsf{ m = \frac{13-(-8)}{2-(-5)} }$

$\mathsf{ m = \frac{21}{7} = 3 }$

(-2,8) (-4,8)

x₁, y₁	x₂, y₂
(-2,8)	(-4,8)

$\mathsf{ m = \frac{8-8}{-4-(-2)} }$

$\mathsf{ m = \frac{0}{-2} = 0 }$

(18,18) (18,23)

x₁, y₁	x₂, y₂
(18,18)	(18,23)

$\mathsf{ m = \frac{23-18}{18-18} }$

$\mathsf{ m = \frac{5}{0} = undefined }$

(-2,-2) (4,-5)

x₁, y₁	x₂, y₂
(-2,-2)	(4,-5)

$\mathsf{ m = \frac{-5-(-2)}{4-(-2)} }$

$\mathsf{ m = \frac{-3}{6} = -\frac{1}{2} }$

(21,14) (24,7)

x₁, y₁	x₂, y₂
(21,14)	(24,7)

$\mathsf{ m = \frac{7-14}{24-21} }$

$\mathsf{ m = -\frac{7}{3} }$

(-5,5) (-2,3)

x₁, y₁	x₂, y₂
(-5,5)	(-2,3)

$\mathsf{ m = \frac{3-5}{-2-(-5)} }$

$\mathsf{ m = -\frac{2}{3} }$

(0,0) (4,4)

x₁, y₁	x₂, y₂
(0,0)	(4,4)

$\mathsf{ m = \frac{4-0}{4-0} }$

$\mathsf{ m = \frac{4}{4} = 1 }$

(19,-5) (25,-5)

x₁, y₁	x₂, y₂
(19,-5)	(25,-5)

$\mathsf{ m = \frac{-5-(-5)}{25-19} }$

$\mathsf{ m = \frac{0}{6} = 0 }$

Now you try!