3 4. What is the slope of the line that passes through (-2, 1) and (8,5)?

      The question gives us two points, (-2, 1) and (8,5), from which we can find the slope and later the equation of the line.

Finding the Slope

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)      

                                          =  (5 - 1) ÷ (8 - (-2))    

                                          =   ⁴/₁₀

                                          = ²/₅  

Checking my

We can check to see if the answer is correct by drawing the line and seeing if it passes through both points. If it does, then the slope is correct.

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

                                ⇒  y - 1 =  ²/₅ (x + 2)

In the graph below (created using Desmos), the line passes through both points. This suggests that we calculated the slope correctly.