Question

Find the equation of the line passing through the points (2,-17) and (6,-19). Write your answer in the form Y=mx+b

Answer 1

The equation of a line between two points is given by:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

plugging the values given we have:

$\begin{gathered} y-(-17)=\frac{-19-(-17)}{6-2}(x-2) \\ y+17=\frac{-19+17}{6-2}(x-2) \\ y+17=-\frac{2}{4}(x-2) \\ y+17=-\frac{1}{2}(x-2) \\ y+17=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1-17 \\ y=-\frac{1}{2}x-16 \end{gathered}$

Therefore the equation of the line is:

$y=-\frac{1}{2}x-16$