Question

for each line, determine whether the slope is positive, negative, zero, or undefined. line 1 try one last time zero negative positive line 2 positive negative zero undefined line 3 undefined positive negative zero line 4 negative positive zero undefined

Explanation:

To determine the slope of each line, we use the concept of slope:

• Horizontal line (Line 1): Slope is \( 0 \) (since \( \text{slope} = \frac{\Delta y}{\Delta x} \), and \( \Delta y = 0 \) for horizontal lines).
• Line with upward trend (Line 2): As \( x \) increases, \( y \) increases, so slope is positive.
• Vertical line (Line 3): Slope is undefined (since \( \Delta x = 0 \), and division by zero is undefined).
• Line with downward trend (Line 4): As \( x \) increases, \( y \) decreases, so slope is negative.

Line 1

Step1: Identify line type

Line 1 is horizontal (parallel to the \( x \)-axis).

Step2: Apply slope formula

Slope \( = \frac{\text{change in } y}{\text{change in } x} \). For a horizontal line, \( \text{change in } y = 0 \), so \( \text{slope} = \frac{0}{\Delta x} = 0 \).

Step1: Analyze direction

Line 2 rises from left to right (as \( x \) increases, \( y \) increases).

Step2: Determine slope sign

A line that rises from left to right has a positive slope.

Step1: Identify line type

Line 3 is vertical (parallel to the \( y \)-axis).

Step2: Apply slope formula

Slope \( = \frac{\text{change in } y}{\text{change in } x} \). For a vertical line, \( \text{change in } x = 0 \), so \( \text{slope} = \frac{\Delta y}{0} \), which is undefined.

Answer:

Zero

Line 2