Question

determine whether the slope of each line is positive, negative, zero, or undefined
positive slope negative slope slope of 0 undefined slope
(three graphs of lines on coordinate planes are shown)

Explanation:

To determine the slope type for each line, we analyze the direction of the line:

First Line (Left Graph):

A line that falls from left to right has a negative slope (as \( y \)-values decrease as \( x \)-values increase).

Second Line (Middle Graph):

A horizontal line (parallel to the \( x \)-axis) has a slope of 0 (since there is no vertical change, \( \text{slope} = \frac{\Delta y}{\Delta x} = \frac{0}{\Delta x} = 0 \)).

Third Line (Right Graph):

A vertical line (parallel to the \( y \)-axis) has an undefined slope (since there is no horizontal change, \( \text{slope} = \frac{\Delta y}{\Delta x} = \frac{\Delta y}{0} \), which is undefined).

Matching to Categories:

• Negative slope: Drag the left graph (falling line) to "Negative slope".
• Slope of 0: Drag the middle graph (horizontal line) to "Slope of 0".
• Undefined slope: Drag the right graph (vertical line) to "Undefined slope".

(Note: The "Positive slope" category would apply to a line that rises from left to right, but none of the shown graphs fit that here.)

Answer:

To determine the slope type for each line, we analyze the direction of the line:

First Line (Left Graph):

A line that falls from left to right has a negative slope (as \( y \)-values decrease as \( x \)-values increase).

Second Line (Middle Graph):

A horizontal line (parallel to the \( x \)-axis) has a slope of 0 (since there is no vertical change, \( \text{slope} = \frac{\Delta y}{\Delta x} = \frac{0}{\Delta x} = 0 \)).

Third Line (Right Graph):

A vertical line (parallel to the \( y \)-axis) has an undefined slope (since there is no horizontal change, \( \text{slope} = \frac{\Delta y}{\Delta x} = \frac{\Delta y}{0} \), which is undefined).

Matching to Categories:

• Negative slope: Drag the left graph (falling line) to "Negative slope".
• Slope of 0: Drag the middle graph (horizontal line) to "Slope of 0".
• Undefined slope: Drag the right graph (vertical line) to "Undefined slope".

(Note: The "Positive slope" category would apply to a line that rises from left to right, but none of the shown graphs fit that here.)