Question

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

Explanation:

Line 1:

A vertical line has an undefined slope because the change in \( x \) (run) is \( 0 \), and slope is \( \frac{\text{rise}}{\text{run}} \), division by zero is undefined. So Line 1: Undefined.

Line 2:

A line that goes up from left to right has a positive slope. As \( x \) increases, \( y \) increases, so the slope \( \frac{\text{rise}}{\text{run}} \) is positive. So Line 2: Positive.

Line 3:

A horizontal line has a slope of zero because the change in \( y \) (rise) is \( 0 \), so \( \frac{0}{\text{run}} = 0 \). So Line 3: Zero.

Line 4:

A line that goes down from left to right has a negative slope. As \( x \) increases, \( y \) decreases, so the slope \( \frac{\text{rise}}{\text{run}} \) (rise is negative here) is negative. So Line 4: Negative.

Answer:

Line 1: Undefined
Line 2: Positive
Line 3: Zero
Line 4: Negative