Complete the equation of the line through (2,1) and (5,-8) Use exact numbers

Given two points (x₁, y₁) and (x₂, y₂), the slope of the line that passes through these two points is given by the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now, for our problem, we identify these two points:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ (x_2,y_2)=(5,-8) \end{gathered}[/tex]Using the previous equation to calculate the slope of the line:
[tex]\begin{gathered} m=\frac{-8-1}{5-2}=\frac{-9}{3} \\ \Rightarrow m=-3 \end{gathered}[/tex]Now, using the point-slope form of the line equation:
[tex](y-y_0)=m(x-x_0)[/tex]Where (x₀, y₀) is any point of the line. Choosing (2, 1) as (x₀, y₀):
[tex]\begin{gathered} (y-1)=-3(x-2) \\ y=-3x+6+1 \\ \therefore y=-3x+7 \end{gathered}[/tex]