Question

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

Explanation:

Step1: Recall slope - concept

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}$. If a line rises from left - to - right, $m>0$; if it falls from left - to - right, $m < 0$; if it is horizontal, $m = 0$; if it is vertical, $m$ is undefined.

Step2: Analyze Line 1

Line 1 falls from left - to - right. So, $\frac{\Delta y}{\Delta x}<0$, and the slope is negative.

Step3: Analyze Line 2

Line 2 is vertical. For a vertical line, $\Delta x = 0$, and the formula for slope $m=\frac{\Delta y}{\Delta x}$ results in division by zero. So, the slope is undefined.

Step4: Analyze Line 3

Line 3 is horizontal. For a horizontal line, $\Delta y=0$, and $m = \frac{0}{\Delta x}=0$ (where $\Delta x
eq0$). So, the slope is zero.

Step5: Analyze Line 4

Line 4 falls from left - to - right. So, $\frac{\Delta y}{\Delta x}<0$, and the slope is negative.

Answer:

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