Question

drag a graph to each category based on the slope of the graph.
slope is between 0 and 1
drag and drop an item here
slope is greater than 1
drag and drop an item here
slope is less than 0
drag and drop an item here
slope is 0
drag and drop an item here

Explanation:

Step1: Recall slope concepts

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Positive slope: line rises from left to right (\( m>0 \)); negative slope: line falls from left to right (\( m<0 \)); slope 0: horizontal line; slope between 0 and 1: gentle rise (rise < run); slope >1: steep rise (rise > run).

Step2: Analyze each graph

• Top graph: Line rises from left to right (positive slope). Let's estimate rise/run. If from (0,0) to (4,2), slope \( \frac{2}{4}=0.5 \) (between 0 and 1? Wait, no—wait, maybe coordinates: if it's steeper? Wait, no, let's recheck. Wait, maybe the first graph (top) has slope >1? Wait, no, let's list each:

1. Top graph (first): Line goes from (0,0) to (3,6)? Wait, no, grid. Let's assume grid squares. If a line has rise > run (e.g., rise 3, run 1: slope 3 >1) or rise < run. Wait, maybe:

• Graph 1 (top): Slope greater than 1 (steep rise, rise > run).
• Graph 2 (second): Slope less than 0 (falls from left to right? Wait, no, second graph: line is almost horizontal but? Wait, no, second graph: line goes from left (negative x) to right (positive x), but is it falling? Wait, no, maybe I missee. Wait, the problem has 5 graphs:

Wait, the categories are:

• Slope between 0 and 1: gentle rise (rise < run)
• Slope greater than 1: steep rise (rise > run)
• Slope less than 0: falling (negative slope)
• Slope is 0: horizontal line

Let's identify each graph:

1. Top graph (first): Line passes through origin, rises steeply (rise > run) → slope >1.
2. Second graph: Line falls from left to right? Wait, no, second graph: line is like a horizontal line? No, wait, second graph: maybe slope <0 (falling). Wait, no, let's correct:

• Graph 1 (top): Positive slope, steep (slope >1)
• Graph 2 (second): Negative slope (falls left to right) → slope <0
• Graph 3 (third): Horizontal line → slope =0
• Graph 4 (fourth): Positive slope, gentle (rise < run) → slope between 0 and 1
• Graph 5 (fifth): Vertical line? No, fifth graph: vertical line? No, fifth graph: vertical line has undefined slope, but here it's a vertical line? Wait, no, fifth graph: vertical line (x=constant) has undefined slope, but in the options, slope is 0 is horizontal. Wait, fifth graph: vertical line? No, the fifth graph is a vertical line? Wait, no, the fifth graph: line is vertical (parallel to y-axis) → undefined slope, but maybe it's a horizontal line? Wait, no, the fourth category is "Slope is 0" (horizontal line). So:

• Slope between 0 and 1: Graph 4 (gentle rise, rise < run)
• Slope greater than 1: Graph 1 (steep rise, rise > run)
• Slope less than 0: Graph 2 (falls left to right)
• Slope is 0: Graph 3 (horizontal line)
• Graph 5: Vertical line (undefined, but maybe it's a vertical line, but slope 0 is horizontal. Wait, maybe I made a mistake. Let's re-express:

Wait, the correct drag-and-drop:

• Slope between 0 and 1: Graph 4 (fourth graph, gentle rise)
• Slope greater than 1: Graph 1 (top, steep rise)
• Slope less than 0: Graph 2 (second, falling)
• Slope is 0: Graph 3 (third, horizontal)
• Graph 5: Maybe vertical, but slope 0 is horizontal, so Graph 3 is horizontal (slope 0).

So:

• Slope between 0 and 1: Drag Graph 4 (fourth)
• Slope greater than 1: Drag Graph 1 (top)
• Slope less than 0: Drag Graph 2 (second)
• Slope is 0: Drag Graph 3 (third)
• The fifth graph (vertical) has undefined slope, but maybe it's a mistake, but according to categories, slope 0 is horizontal (Graph 3), slope <0 is Graph 2, slope >1 is Graph 1, slope between 0-1 is Graph 4, and slope 0 is Graph 3.

Answer:

• Slope between 0 and 1: The fourth graph (from top)
• Slope greater than 1: The first graph (top)
• Slope less than 0: The second graph (from top)
• Slope is 0: The third graph (from top)