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

Answer:

            $\bold{m_1=-\dfrac38}$

            $\bold{m_2=\dfrac12}$

            $\bold{m_3=-1\dfrac12}$

Step-by-step explanation:

The slope of the line passing through two given points:  $m=\dfrac{y_2-y_1}{x_2-x_1}$

(0, 5)   ⇒   x₁ = 0,  y₁ = 5

(8, 2)   ⇒     x₂ = 8,  y₂ = 2

So, the slope:

                     $m_1=\dfrac{2-5}{8-0}=\dfrac{-3}{8}=-\dfrac38$

(2, -1)   ⇒   x₁ = 2,  y₁ = -1

(6, 1)   ⇒     x₂ = 6,  y₂ = 1

The slope:

                     $m_2=\dfrac{1-(-1)}{6-2}=\dfrac{2}{4}=\dfrac12$

(-3, -2)   ⇒   x₁ = -3,  y₁ = -2

(-1, -5)   ⇒     x₂ = -1,  y₂ = -5

The slope:

                     $m_3=\dfrac{-5-(-2)}{-1-(-3)}=\dfrac{-3}{2}=-\dfrac32=-1\frac12$