Question

What is an equation of the line that passes through the points (4,7) and (2,-1)? Answer in fully reduced form.

Answer 1

The eqaution 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 our points we have:

$\begin{gathered} y-(-7)=\frac{-1-(-7)}{2-4}(x-4) \\ y+7=\frac{6}{-2}(x-4) \\ y+7=-3(x-4) \\ y+7=-3x+12 \\ y=-3x+12-7 \\ y=-3x+5 \end{gathered}$

Therefore the equation is:

$y=-3x+5$