May you please help me understand how to do this? Thanks

Give the slope of a line perpendicular to the given line.

1. y=3x+5

slope of this line is 3.

the slope of the perpendicular is the negative recirpocal, or -1/3

Oh ok I get it. Is there any work to show to get this answer?

Certainly! To find the slope of a line perpendicular to a given line, we need to recall that perpendicular lines have slopes that are negative reciprocals of each other.

Let's start by finding the slope of the given line, y = 3x + 5.

The equation is in the form y = mx + b, where m is the slope. In this case, the slope is 3.

To find the slope of a line perpendicular to this line, we take the negative reciprocal of 3. The negative reciprocal is when we flip the fraction and change its sign.

So, the slope of a line perpendicular to the given line y = 3x + 5 would be -1/3.