Question

What is the slope of the line containing the points left parenthesis 1 comma 4 right parenthesis(1,4) and left parenthesis 5 comma 1 right parenthesis question mark (5,1)? select the correct choice below and fill in any answer boxes within your choice?

Answer 1

If you know the coordinates of two points

$P = (P_x, P_y),\quad Q = (Q_x, Q_y)$

of two points, the slope of the line passing through them is given by

$\dfrac{P_y-Q_y}{P_x-Q_x}$

So, if we choose in this example

$P = (1,4),\quad Q = (5,1)$

The slope is

$\dfrac{4-1}{1-5} = \dfrac{3}{-4} = -\dfrac{3}{4}$