Question

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

Explanation:

Step1: Recall slope concept

The slope of a line is $m=\frac{y_2 - y_1}{x_2 - x_1}$. If a line rises from left - to - right, $m>0$; if it is horizontal, $m = 0$; if it falls from left - to - right, $m<0$; and if it is vertical, the slope is undefined.

Step2: Analyze Line 1

Line 1 rises from left to right. So, the slope is positive.

Step3: Analyze Line 2

Line 2 is a horizontal line. For a horizontal line, the change in $y$ ($\Delta y$) between any two points is 0. Using the slope formula $m=\frac{\Delta y}{\Delta x}$, when $\Delta y = 0$, $m = 0$.

Step4: Analyze Line 3

Line 3 is a vertical line. For a vertical line, the change in $x$ ($\Delta x$) between any two points is 0. Since division by 0 is undefined in the slope formula $m=\frac{\Delta y}{\Delta x}$, the slope is undefined.

Step5: Analyze Line 4

Line 4 rises from left to right. So, the slope is positive.

Answer:

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