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

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

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

Answer

Explanation:

Step1: Recall slope - determination rule

The slope of a line is calculated as $m=\frac{\Delta y}{\Delta x}$. If the line rises from left to right, $\Delta y>0$ and $\Delta x>0$, so $m > 0$; if it falls from left to right, $\Delta y<0$ and $\Delta x>0$, so $m<0$; if it is horizontal, $\Delta y = 0$, so $m = 0$; if it is vertical, $\Delta x=0$ and the slope is undefined.

Step2: Analyze Line 1

Line 1 rises from left to right. As $x$ increases, $y$ increases. So the slope $m=\frac{\Delta y}{\Delta x}>0$.

Step3: Analyze Line 2

Line 2 is a vertical line. For a vertical line, the change in $x$ ($\Delta x$) between any two points is 0. Since the slope formula $m = \frac{\Delta y}{\Delta x}$ and division by zero is undefined, the slope of Line 2 is undefined.

Step4: Analyze Line 3

Line 3 rises from left to right. As $x$ increases, $y$ increases. So the slope $m=\frac{\Delta y}{\Delta x}>0$.

Step5: Analyze Line 4

Line 4 is a horizontal line. For a horizontal line, the change in $y$ ($\Delta y$) between any two points is 0. So the slope $m=\frac{\Delta y}{\Delta x}=0$.

Answer:

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