What is the gradient of a horizontal line?

What is the gradient of a horizontal line?

• A. 0
• B. 1
• C. Undefined
• D. Negative infinity

Answer: (A)

A horizontal line is one that runs parallel to the x-axis. This means that as the value of \( x \) increases or decreases, the value of \( y \) remains constant. To determine the gradient (or slope) of a line, we use the formula: \[ \text{slope} = \frac{\Delta y}{\Delta x} \] where \( \Delta y \) is the change in the y-value and \( \Delta x \) is the change in the x-value. For a horizontal line, \( \Delta y \) is always 0 because there is no change in the y-value regardless of changes in the x-value. Therefore, the formula becomes: \[ \text{slope} = \frac{0}{\Delta x} = 0 \] This results in a gradient of 0, indicating that the line is flat and does not rise or fall. In this context, the choice indicating a gradient of 0 reflects the fundamental property of horizontal lines in coordinate geometry, reinforcing the understanding that horizontal lines have no slope. This is why the correct answer is identified as 0.

A horizontal line is one that runs parallel to the x-axis. This means that as the value of ( x ) increases or decreases, the value of ( y ) remains constant.

To determine the gradient (or slope) of a line, we use the formula:

[

\text{slope} = \frac{\Delta y}{\Delta x}

]

where ( \Delta y ) is the change in the y-value and ( \Delta x ) is the change in the x-value. For a horizontal line, ( \Delta y ) is always 0 because there is no change in the y-value regardless of changes in the x-value. Therefore, the formula becomes:

[

\text{slope} = \frac{0}{\Delta x} = 0

]

This results in a gradient of 0, indicating that the line is flat and does not rise or fall. In this context, the choice indicating a gradient of 0 reflects the fundamental property of horizontal lines in coordinate geometry, reinforcing the understanding that horizontal lines have no slope. This is why the correct answer is identified as 0.