Answer:
y = -x / 3
Step-by-step explanation:
For this problem, it is important to note two things. We want our equation to be perpendicular to the function y = 3x + 2, and we want it to pass through the origin (0,0). With this in mind, let's begin.
To create an equation that is perpendicular to another linear function, we simply will apply the idea of a negative reciprocal to the slope of said function. Note, we are given that the function we wish to be perpendicular to has a slope of 3, as denoted in the slope-intercept form's x coefficient.
So, our function should be the negative reciprocal of this function's slope. So the negative reciprocal of 3 is -1/3. When these two slopes meet, they will form a 90-degree angle which by definition, means they are perpendicular.
The second part of this problem wants our function to go through the origin. The most simple way of satisfying this requirement is simply to make the y-intercept 0. This ensures our line will cross through the origin.
From here, let's use our information to write our equation:
y = (-1/3)x + 0
y = -x / 3
Note the bottom equation is a simplification of the top equation, where the top equation is the full slope-intercept form.
Hence, y = -x / 3 is a perpendicular line to y = 3x + 2 that also crosses at the origin.
Cheers.
