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

Let's start with line 1.

`m=(1-13)/(-8-1)\Rightarrow m=(-12)/(-9)\Rightarrow m=(4)/(3)`

The slope of line 1 is 4/3.

Let's move on to line 2.

`m=((5)/(3)-(-1))/(5-3)\Rightarrow m=((8)/(3))/(2)\Rightarrow m=(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.