Question

Is the line through points P(0, 1) and Q(5, 0) parallel to the line through points R(–4, 3) and S(–5, 4)? Explain.

Answer 1

The parallel lines have the same a slope.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have

P(0, 1), Q(5, 0). Substitute:

$m_{PQ}=\dfrac{0-1}{5-0}=\dfrac{-1}{5}=-\dfrac{1}{5}$

R(-4, 3), S(-5, 4). Substitute:

$m_{RS}=\dfrac{4-3}{-5-(-4)}=\dfrac{1}{-5+4}=\dfrac{1}{-1}=-1$

$m_{PQ}\neq m_{RS}$

Therefore the lines PQ and RS are not parallel.