Question

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

Explanation:

Step1: Analyze "Slope is 0"

A slope of 0 means the line is horizontal (constant \( y \)-value). The bottom - most graph (the fourth one) has a horizontal line, so it belongs here.

Step2: Analyze "Slope is less than 0"

A negative slope means the line falls from left to right. The top - most graph (the first one) has a line that decreases as \( x \) increases, so it belongs here.

Step3: Analyze "Slope is greater than 1"

A slope greater than 1 means the line is steeper than a line with slope 1. The third graph has a steeper positive slope (rise over run is greater than 1), and the second graph has a slope of 1 (since it goes through points like (0,0) and (1,1) or similar, slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=1\)). Wait, correction: The second graph has a slope of 1 (line through origin with 45 - degree angle), the third graph has a slope greater than 1 (steeper), so "Slope is greater than 1" gets the third graph, and "Slope is 1" would be the second, but in our categories, "Slope is greater than 1" takes the third, "Slope is less than 0" takes the first, "Slope is 0" takes the fourth. Wait, re - checking:

• Slope 0: horizontal line (fourth graph).
• Slope < 0: line decreasing from left to right (first graph).
• Slope > 1: line with steep positive slope (third graph, because its rise over run is more than 1, e.g., if it goes from (0,0) to (2, - 4)? No, wait, the third graph: let's assume grid is 1 unit per square. If the line goes from (0,0) to (2, - 4)? No, direction: the third graph has a line going from top - left to bottom - right? No, wait, the third graph's line: looking at the axes, if it's a positive slope? Wait, no, the third graph: maybe I misread. Wait, the first graph: two lines crossing? No, the first graph has a line with negative slope (from top - left to bottom - right). The second graph: line with slope 1 (from bottom - left to top - right, 45 degrees). The third graph: line with slope greater than 1 (steeper, so for a run of 1, rise is more than 1). The fourth graph: horizontal (slope 0). So:
• "Slope is 0": Fourth graph (bottom one).
• "Slope is less than 0": First graph (top one).
• "Slope is greater than 1": Third graph (the one above the bottom - most). The second graph has slope 1, so it's not in "greater than 1".

Answer:

• "Slope is 0": The bottom - most (fourth) graph.
• "Slope is less than 0": The top - most (first) graph.
• "Slope is greater than 1": The third graph (above the bottom - most).