Question

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

Explanation:

Step1: Recall slope - definition

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Analyze Line 1

As $x$ increases, $y$ increases. So $m=\frac{\Delta y}{\Delta x}>0$, slope is positive.

Step3: Analyze Line 2

It is a vertical line. For vertical lines, $x_2 - x_1 = 0$, and $m=\frac{y_2 - y_1}{0}$ is undefined.

Step4: Analyze Line 3

As $x$ increases, $y$ increases. So $m=\frac{\Delta y}{\Delta x}>0$, slope is positive.

Step5: Analyze Line 4

As $x$ changes, $y$ remains the same. So $m=\frac{0}{\Delta x}=0$, slope is zero.

Answer:

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