What can be concluded about the gradient of a horizontal line?

What can be concluded about the gradient of a horizontal line?

• A. It can be any negative number
• B. It is always equal to zero
• C. It is always a positive number
• D. It approaches infinity

Answer: (B)

A horizontal line is characterized by the fact that it maintains a constant y-value regardless of changes in the x-value. This means that as you move from left to right along the line, there is no change in height; the line does not rise or fall. The gradient, or slope, of a line is calculated as the change in y divided by the change in x. For a horizontal line, since there is no change in y (it remains constant), the change in y equals zero. Therefore, the formula for the gradient, which is \(\frac{\text{change in } y}{\text{change in } x}\), results in \(\frac{0}{\text{change in } x}\). This simplifies to zero, confirming that the gradient of a horizontal line is always equal to zero.

A horizontal line is characterized by the fact that it maintains a constant y-value regardless of changes in the x-value. This means that as you move from left to right along the line, there is no change in height; the line does not rise or fall. The gradient, or slope, of a line is calculated as the change in y divided by the change in x. For a horizontal line, since there is no change in y (it remains constant), the change in y equals zero.

Therefore, the formula for the gradient, which is (\frac{\text{change in } y}{\text{change in } x}), results in (\frac{0}{\text{change in } x}). This simplifies to zero, confirming that the gradient of a horizontal line is always equal to zero.