Question

the graph represents the heights of two climbers on a climbing wall over a 12 - minute time period. which statement is true about the climbers’ heights? the climbing wall graph with time (min) on x - axis from 0 to 12 and height (feet) on y - axis from 0 to 24, showing abby’s climb and brynn’s climb
options:

• brynn was resting at a constant climbing height when abby’s climbing height was decreasing.
• abby’s climbing height was decreasing when brynn’s climbing height was increasing.
• the heights of both climbers increased, then decreased, with no rest at a constant height.
• both climbers rested on the wall at a constant height for 2 minutes.

Explanation:

Step1: Analyze each option

• Option 1: Check when Abby's height is decreasing (after minute 9 for Abby? Wait, no, Abby's graph: let's see the x-axis (time) and y-axis (height). Abby's climb: starts at (0,4), increases, then maybe rests? Wait, the graph: Abby's line (black) and Brynn's (blue). Let's check the segments:
• For Brynn (blue): starts at (0,0), increases to (5,14)? Wait, no, the grid: each x is 1 minute, y is 2 feet? Wait, the y-axis has 2,4,6,...24. Let's look at the horizontal segments (constant height, resting). Abby's graph: from minute 5 to 7? Wait, no, the black line (Abby) has a horizontal segment? Wait, the blue line (Brynn) and black (Abby). Let's check each option:
• Option 1: "Brynn was resting at a constant climbing height when Abby's climbing height was decreasing." When is Abby's height decreasing? After minute 9 (Abby's line goes down from 21 to 0 at 12). Brynn's line: from minute 7 to 10? Wait, Brynn's line: after minute 7, does she rest? No, Brynn's line after minute 7: from (7,14) down to (10,0). Wait, maybe I misread. Wait, the graph: Abby's climb (black) has a horizontal segment? Wait, the blue line (Brynn) and black (Abby). Let's re-express:
• Abby's path: (0,4) -> increases to (5,14) -> horizontal (rest) from 5 to 7 (height 14) -> increases to (9,21) -> decreases to (12,0).
• Brynn's path: (0,0) -> increases to (5,14) -> horizontal (rest) from 5 to 7 (height 14) -> decreases to (10,0). Wait, no, the blue line: at minute 5, both are at 14. Then Abby goes up, Brynn rests? Wait, no, the black line (Abby) at minute 7: height 14, then goes up to 21 at minute 9. Brynn's line: at minute 7, height 14, then goes down? Wait, maybe the graph is: Abby (black) starts at (0,4), climbs to (5,14), rests (horizontal) until minute 7, then climbs to (9,21), then descends to (12,0). Brynn (blue) starts at (0,0), climbs to (5,14), rests (horizontal) until minute 7, then descends to (10,0). Wait, but the options:
• Option 4: "Both climbers rested on the wall at a constant height for 2 minutes." Let's check the horizontal segments. Abby: from minute 5 to 7 (2 minutes, height 14). Brynn: from minute 5 to 7 (2 minutes, height 14). Then Abby climbs up, Brynn descends. So this option is true. Let's check other options:
• Option 1: When Abby's height is decreasing (after minute 9), Brynn's height is already decreasing (Brynn is at 0 by minute 10). So Brynn is not resting then.
• Option 2: When Brynn's height is increasing (from 0 to 5 minutes), Abby's height is also increasing (from 4 to 14). So Abby's height is not decreasing then.
• Option 3: "The heights of both climbers increased, then decreased, with no rest at a constant height." But both had horizontal segments (rest) from 5 to 7, so this is false.
• Option 4: Both rested (horizontal) from minute 5 to 7, which is 2 minutes. So this is true.

Step2: Confirm the correct option

After analyzing each option, option 4 ("Both climbers rested on the wall at a constant height for 2 minutes") is true.

Answer:

D. Both climbers rested on the wall at a constant height for 2 minutes (assuming the options are labeled A, B, C, D with D being this option; if the original options are labeled as such, but in the problem, the last option is "Both climbers rested on the wall at a constant height for 2 minutes", so the correct statement is this one.