Final answer:
The counterexample to the statement that a line's slope can only be positive or negative is a horizontal line, which has a slope of zero. This challenges the statement and adds that slopes can also be zero.
Step-by-step explanation:
To counter the statement that 'The slope of a line can only be positive or negative,' the correct choice is a horizontal line. A horizontal line depicts a slope of zero, which is neither positive nor negative. Therefore, the correct answer which serves as a counterexample is:
- c. It is a horizontal line at some negative value.
- d. It is a horizontal line at some positive value.
Both answer choices represent a horizontal line, which regardless of whether it is located at a positive or negative value on the y-axis, will have a slope of zero. This challenges the original statement by showing that a slope can also be zero, in addition to being positive or negative.
As the slope increases, regardless of it being positive or negative, the line gets steeper. A positive slope slants upward from left to right, while a negative slope slants downward. A horizontal line with a slope of zero will be perfectly flat and a vertical line, which is not a function, cannot have a slope and is instead considered undefined because division by zero is not possible.