Final answer:
Line L with a slope of 2/3 is perpendicular to a line with a slope of -3/2, as the negative reciprocal of 2/3 is -3/2. Hence, the correct answer is option E.
Step-by-step explanation:
The question concerns a line L with a given slope of 2/3. For lines in a two-dimensional plane, specific relationships between their slopes indicate whether they are parallel or perpendicular to each other. If two lines are parallel, they will have the same slope. If two lines are perpendicular, the product of their slopes will be -1, implying that the slope of one line is the negative reciprocal of the slope of the other. In this instance, the correct statement regarding the line L is that it is perpendicular to a line with a slope of -3/2. We determine this by taking the negative reciprocal of the slope 2/3, which gives us -3/2. Hence, option E is the true statement. Lines that are horizontal have a slope of 0 and lines that are vertical have an undefined slope, neither of which is relevant to line L with a slope of 2/3.
Therefore, the other options:
- A line with a slope of -2/3 is neither parallel nor perpendicular to line L.
- A horizontal line does not match the given slope of the line L.
- A line perpendicular to L would not have a slope of 3/2, it would have a slope of -3/2.
- A vertical line would not have the slope in the form of a ratio, as vertical lines have an undefined slope.
With this logic, we can confidently select option E as the correct answer.