Question

Prealgebra- Determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither

Answer 1

It is important to note the following:

• If the slopes of the two lines are equal, they are parallel.

,

• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.

Let's now calculate the slope of each line. Use the formula:

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

Let's start with line 1.

$m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}$

The slope of line 1 is 4/3.

Let's move on to line 2.

$m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}$

The slope of line 2 is also 4/3.

Since the slopes of the two lines are the same, then the two lines are parallel.