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 - definition

The slope of a line is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line, $y_2=y_1$.

Step2: Calculate slope of Line 1

For a horizontal line, if we take two points $(x_1,y)$ and $(x_2,y)$ on the line, then $m=\frac{y - y}{x_2 - x_1}=0$.

Step3: Recall vertical - line slope

For a vertical line, $x_2=x_1$. The formula for slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ has a denominator of 0.

Step4: Calculate slope of Line 2

For a vertical line with two points $(x,y_1)$ and $(x,y_2)$, $m=\frac{y_2 - y_1}{x - x}$, which is undefined.

Step5: Analyze downward - sloping line

For a line that goes down 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

Step6: Analyze upward - sloping line

For a line that goes up 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