Question

Is the line through points P(3, -5) and 2(1, 4) parallel to the line through points R(-1, 1) and S(3,Explain.

Answer 1

As given by the question

There are given that the two-point;

$\begin{gathered} P(3,\text{ -5) and Q(1, 4)} \\ R(-1,\text{ 1) and S(3, -3)} \end{gathered}$

Now,

First, find the slope of both of the lines from the point

Then,

For first line:

$\begin{gathered} PQ(m)=\frac{y_2-y_1}{x_2-x_1} \\ PQ(m)=\frac{4_{}+5_{}}{1_{}-3_{}} \\ PQ(m)=\frac{9}{-2} \\ PQ(m)=-\frac{9}{2} \end{gathered}$

Now,

For the second line:

$\begin{gathered} RS(m)=\frac{y_2-y_1}{x_2-x_1} \\ RS(m)=\frac{-3_{}-1_{}}{3_{}+1_{}} \\ RS(m)=-\frac{4}{4} \\ RS(m)=-1 \end{gathered}$

Since both slopes are different, they are not parallel lines, which means parallel lines have the same slope.

Hence, the correct optio