Question

the graph of a linear function is shown. which word describes the slope of the line? positive negative zero undefined

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is calculated as \( m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Identify points on the line

From the graph, the line is horizontal (parallel to the x - axis). Let's take two points, say \( (0, - 3) \) and \( (1, - 3) \).

Step3: Calculate \( \Delta y \) and \( \Delta x \)

For the points \( (0,-3) \) and \( (1,-3) \), \( \Delta y=-3-(-3) = 0 \) and \( \Delta x=1 - 0=1 \).

Step4: Calculate slope

Using the slope formula \( m=\frac{\Delta y}{\Delta x}=\frac{0}{1}=0 \). A horizontal line has a slope of zero.

Answer:

zero (The option corresponding to "zero" in the multiple - choice options, which is the third option: zero)