Question

use the drawing tool(s) to form the correct answer on the provided graph.
paul and his neighbors decided to build a fence along his farm. after three hours, they have 15 meters of fencing complete. they decide to take a 2 - hour break for lunch and then resume building the fence. after four more hours, they have a fence that is a total of 55 meters long.
construct the graph that models the given situation.

Explanation:

Step 1: Identify Key Time - Length Points

• At \(x = 0\) (start), \(y = 0\) (no fencing).
• After 3 hours (\(x = 3\)), \(y = 15\) meters.
• During the 2 - hour lunch break, time increases from \(x = 3\) to \(x = 3+2 = 5\), but length (\(y\)) stays at 15 meters.
• After 4 more hours (total time \(x = 5 + 4=9\)), \(y = 55\) meters.

Step 2: Draw Segments

• First Segment: Connect \((0, 0)\) to \((3, 15)\) (represents the first 3 hours of building).
• Second Segment: Connect \((3, 15)\) to \((5, 15)\) (horizontal line for the lunch break, as length doesn't change).
• Third Segment: Connect \((5, 15)\) to \((9, 55)\) (represents the 4 hours of building after the break).

Answer:

To construct the graph:

1. First Segment (Building Phase 1): Plot the point \((3, 15)\) (3 hours, 15 meters) and draw a line from \((0, 0)\) to \((3, 15)\) (assuming work starts at \(x = 0\), \(y = 0\)).
2. Second Segment (Lunch Break): Draw a horizontal line from \((3, 15)\) to \((5, 15)\) (2 - hour break: \(3 + 2 = 5\) hours, length remains 15 meters).
3. Third Segment (Building Phase 2): Plot the point \((9, 55)\) (5 hours + 4 hours = 9 hours, 55 meters) and draw a line from \((5, 15)\) to \((9, 55)\).