Question

Find the slope of the line that passes through the following sets of points. Write your answer in simplest form.

(0, 5) and (8, 2)

(2, -1) and (6, 1)

(-3, -2) and (-1, -5)

Answer 1

`\bold{m_1=-\frac38}`

`\bold{m_2=\frac12}`

`\bold{m_3=-1\frac12}`

Explanation:

The slope of the line passing through two given points:
`m=(y_2-y_1)/(x_2-x_1)`

(0, 5) ⇒ x₁ = 0, y₁ = 5

(8, 2) ⇒ x₂ = 8, y₂ = 2

So, the slope:

`m_1=(2-5)/(8-0)=(-3)/(8)=-\frac38`

(2, -1) ⇒ x₁ = 2, y₁ = -1

(6, 1) ⇒ x₂ = 6, y₂ = 1

The slope:

`m_2=(1-(-1))/(6-2)=(2)/(4)=\frac12`

(-3, -2) ⇒ x₁ = -3, y₁ = -2

(-1, -5) ⇒ x₂ = -1, y₂ = -5

The slope:

`m_3=(-5-(-2))/(-1-(-3))=(-3)/(2)=-\frac32=-1\frac12`