Aline through the origin has a slope of 1 / 3. carlos thinks the slope of a perpendicular line at the origin will be 3.
do you agree? explain why or why not.

Carlos is incorrect.

Step-by-step explanation:

We have been given that a line through the origin has a slope of . Carlos thinks the slope of a perpendicular line at the origin will be 3.

We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.

The slope of the perpendicular line at the origin will be negative reciprocal of .

Let us find negative reciprocal of as:

Since the slope of a perpendicular line at the origin is , therefore, Carlos is incorrect.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x