Question

for each line, determine whether the slope is positive, negative, zero, or undefined. line 1 (graph with horizontal line) options: positive, negative, zero, undefined. line 2 (graph with vertical line) options: positive, negative, zero, undefined. line 3 (graph with falling line) options: positive, negative, zero, undefined. line 4 (graph with rising line) options: positive, negative, zero, undefined.

Explanation:

Line 1

Step1: Recall slope definition

Slope \( m=\frac{\Delta y}{\Delta x} \). For a horizontal line, \( \Delta y = 0 \) (change in y - value is zero as y remains constant).

Step2: Calculate slope

If \( \Delta y = 0 \), then \( m=\frac{0}{\Delta x}=0 \) (where \( \Delta x
eq0 \) for a horizontal line, but since numerator is 0, slope is 0).

Step1: Recall slope definition

Slope \( m = \frac{\Delta y}{\Delta x} \). For a vertical line, \( \Delta x=0 \) (change in x - value is zero as x remains constant).

Step2: Analyze division by zero

Division by zero is undefined in mathematics. So when \( \Delta x = 0 \), the slope \( m=\frac{\Delta y}{0} \) is undefined.

Step1: Recall slope definition

Slope \( m=\frac{\Delta y}{\Delta x} \). For a line that goes from top - left to bottom - right (decreasing as x increases), \( \Delta y<0 \) and \( \Delta x > 0 \) (or vice - versa, but the ratio will be negative).

Step2: Determine sign of slope

If \( \Delta y<0 \) and \( \Delta x>0 \), then \( m=\frac{\Delta y}{\Delta x}<0 \), so the slope is negative.

Answer:

Zero

Line 2