Explain how to write an equation of the line that passes through the point (3,1) and is a parallel to the line y=5 and (b) perpendicular to the line y=5

The parallel line would be y = 1 and the perpendicular line would be x = 3.

Step-by-step explanation:

In order to find a line parallel to y = 5, we must first note that y = 5 is a horizontal line. This means to be parallel, the line must also be horizontal. All horizontal lines are written in the form of y = (just a number). Since we can see the value of y in the ordered pair as 1, we know the equation is y = 1.

The exact opposite logic can be used to find the perpendicular line. Since the first line is horizontal, the next one will be vertical, which are written as x = (a number). We again look to the ordered pair to determine the number and write the equation as x = 3