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

for each line, determine whether the slope is positive, negative, zero, or undefined.\nline 1\nline 2\nline 3\nline 4\npositive\npositive\npositive\npositive\nnegative\nnegative\nnegative\nnegative\nzero\nzero\nzero\nzero\nundefined\nundefined\nundefined\nundefined

for each line, determine whether the slope is positive, negative, zero, or undefined.\nline 1\nline 2\nline 3\nline 4\npositive\npositive\npositive\npositive\nnegative\nnegative\nnegative\nnegative\nzero\nzero\nzero\nzero\nundefined\nundefined\nundefined\nundefined

Answer

Explanation:

Step1: Recall slope - rise over run concept

The slope $m$ of a line is given by $m=\frac{\text{rise}}{\text{run}}=\frac{y_2 - y_1}{x_2 - x_1}$. A positive - slope line rises from left to right, a negative - slope line falls from left to right, a zero - slope line is horizontal, and an undefined - slope line is vertical.

Step2: Analyze Line 1

Line 1 falls from left to right. So, its slope is negative.

Step3: Analyze Line 2

Line 2 rises from left to right. So, its slope is positive.

Step4: Analyze Line 3

Line 3 is horizontal. For a horizontal line, $y_2=y_1$, so $m = \frac{y_2 - y_1}{x_2 - x_1}=0$. Its slope is zero.

Step5: Analyze Line 4

Line 4 is vertical. For a vertical line, $x_2=x_1$, and the formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ has a denominator of 0, making the slope undefined.

Answer:

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