Question

for each 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 - definition

The slope of a line is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. A horizontal line has a slope of 0, a vertical line has an undefined slope, a line rising from left - to - right has a positive slope, and a line falling from left - to - right has a negative slope.

Step2: Analyze Line 1

Line 1 is a horizontal line. For any two points $(x_1,y_1)$ and $(x_2,y_2)$ on a horizontal line, $y_1=y_2$. So, $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0}{x_2 - x_1}=0$.

Step3: Analyze Line 2

Line 2 is a vertical line. For any two points $(x_1,y_1)$ and $(x_2,y_2)$ on a vertical line, $x_1 = x_2$. Then $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{y_2 - y_1}{0}$, which is undefined.

Step4: Analyze Line 3

Line 3 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

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: Undefined
Line 3: Negative
Line 4: Positive