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

for each line, determine whether the slope is positive, negative, zero, or undefined. line 1 line 2 line 3 line 4 positive positive positive positive negative negative negative negative zero zero zero zero undefined undefined undefined undefined
Answer
Explanation:
Step1: Recall slope - definition
The slope $m$ of a line is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$ for two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line. A horizontal line has $y_2=y_1$, a vertical line has $x_2 = x_1$, a line rising from left - to - right has $y_2>y_1$ when $x_2>x_1$, and a line falling from left - to - right has $y_2<y_1$ when $x_2>x_1$.
Step2: Analyze Line 1
Line 1 is a horizontal line. For any two points on a horizontal line, $y_2 - y_1=0$. So, $m = \frac{0}{x_2 - x_1}=0$ (assuming $x_2\neq x_1$).
Step3: Analyze Line 2
Line 2 is falling from left to right. If we take two points $(x_1,y_1)$ and $(x_2,y_2)$ with $x_2>x_1$, then $y_2<y_1$. So, $m=\frac{y_2 - y_1}{x_2 - x_1}<0$.
Step4: Analyze Line 3
Line 3 is a horizontal line. For any two points on it, $y_2 - y_1 = 0$. So, $m=\frac{0}{x_2 - x_1}=0$ (assuming $x_2\neq x_1$).
Step5: Analyze Line 4
Line 4 is rising from left to right. If we take two points $(x_1,y_1)$ and $(x_2,y_2)$ with $x_2>x_1$, then $y_2>y_1$. So, $m=\frac{y_2 - y_1}{x_2 - x_1}>0$.
Answer:
Line 1: Zero Line 2: Negative Line 3: Zero Line 4: Positive