Question

for each line, determine whether the slope is positive, negative, zero, or undefined.
line 1
line 2
line 3
line 4
positive
negative
zero
undefined
positive
negative
zero
undefined
positive
negative
zero
undefined
positive
negative
zero
undefined

Explanation:

Line 1:

A vertical line has an undefined slope because the slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$, and for a vertical line, $x_2 - x_1 = 0$, which makes the slope undefined. So Line 1 has an undefined slope.

Line 2:

As we move from left to right, the line is decreasing (going downwards). A line with a negative slope decreases from left to right. So Line 2 has a negative slope.

Line 3:

As we move from left to right, the line is increasing (going upwards). A line with a positive slope increases from left to right. So Line 3 has a positive slope.

Line 4:

A horizontal line has a slope of zero because the change in $y$ ($y_2 - y_1$) is zero. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, if $y_2 - y_1 = 0$, then $m = 0$. So Line 4 has a zero slope.

Answer:

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