Question

for each line, determine whether the slope is positive, negative, zero, or undefined.
line 1\tline 2\tline 3\tline 4
graphs of line 1 (rising from left to right), line 2 (falling from left to right), line 3 (vertical), line 4 (horizontal)
positive
negative
zero
undefined\tpositive
negative
zero
undefined\tpositive
negative
zero
undefined\tpositive
negative
zero
undefined

Explanation:

Step1: Analyze Line 1

A line with a positive slope rises from left to right. Line 1 rises as x increases, so its slope is positive.

Step2: Analyze Line 2

A line with a negative slope falls from left to right. Line 2 falls as x increases, so its slope is negative.

Step3: Analyze Line 3

A vertical line has an undefined slope (since the change in x is 0, and slope is $\frac{\Delta y}{\Delta x}$, division by zero is undefined). Line 3 is vertical, so its slope is undefined.

Step4: Analyze Line 4

A horizontal line has a slope of zero (since the change in y is 0, slope = $\frac{0}{\Delta x}$ = 0). Line 4 is horizontal, so its slope is zero.

Answer:

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