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:

Step1: Analyze Line 1

Line 1 is decreasing from left to right. A line with a negative slope decreases as we move from left to right. So Line 1 has a negative slope.

Step2: Analyze Line 2

Line 2 is increasing from left to right. A line with a positive slope increases as we move from left to right. So Line 2 has a positive slope.

Step3: Analyze Line 3

Line 3 is a vertical line. The slope of a vertical line is undefined (since the run, or change in x, is 0, and division by 0 is undefined in the slope formula \(m = \frac{\Delta y}{\Delta x}\)). So Line 3 has an undefined slope.

Step4: Analyze Line 4

Line 4 is a horizontal line. The slope of a horizontal line is 0 (since the rise, or change in y, is 0, so \(m=\frac{0}{\Delta x}=0\) as long as \(\Delta x
eq0\)). So Line 4 has a slope of 0.

Answer:

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