Question

Find the equation of a line that contains the points (4,-1) and (-1,-4)

Answer 1

Let:

$\begin{gathered} (x1,y1)=(4,-1) \\ (x2,y2)=(-1,-4) \\ \text{The slope is given by:} \\ \text{Slope}=m=\frac{y2-y1}{x2-x1}=\frac{-4-(-1)}{-1-4}=\frac{-4+1}{-5}=\frac{-3}{-5}=\frac{3}{5} \end{gathered}$

Using the slope point equation:

$\begin{gathered} y-y1=m(x-x1) \\ y-(-1)=\frac{3}{5}(x-4) \\ y+1=\frac{3}{5}x-\frac{12}{5} \\ y=\frac{3}{5}x-\frac{12}{5}-1 \\ y=\frac{3}{5}x-\frac{17}{5} \end{gathered}$