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=(y_2-y_1)/(x_2-x_1)`

We have

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

`m_(PQ)=(0-1)/(5-0)=(-1)/(5)=-(1)/(5)`

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

`m_(RS)=(4-3)/(-5-(-4))=(1)/(-5+4)=(1)/(-1)=-1`

`m_(PQ)\\eq m_(RS)`

Therefore the lines PQ and RS are not parallel.