Green plants live in the ocean at maximum and minimum depths described by the absolute value equation |15-d|-15=0, where d is depth, in meters. Graph the equation on a number line to determine the maximum and minimum depths at which green plants live in the ocean.
|15-d|-15=0
|15-d| = 15
so you want |15-d| ≤ 15
15-d ≤ 15 and -15 + d ≤ 15
-d ≤ 0 and d ≤ 30
d ≥ 0 and d ≤ 30
0 ≤ d ≤ 30
To graph the absolute value equation |15 - d| - 15 = 0 on a number line, you need to solve it first. Let's break it down step by step.
Step 1: Move -15 to the other side of the equation, so it becomes |15 - d| = 15.
Step 2: Split the equation into two separate cases, one for the positive value inside the absolute value and one for the negative value. We'll solve each case independently.
Case 1: 15 - d = 15 (positive value)
In this case, the absolute value is 15 - d, so we have 15 - d = 15. Solve for d: subtract 15 from both sides, which gives us -d = 0, or d = 0.
Case 2: 15 - d = -15 (negative value)
In this case, the absolute value is -(15 - d), so we have 15 - d = -15. Solve for d: subtract 15 from both sides, which gives us -d = -30, or d = 30.
Now that we have solved both cases, we know that green plants live in the ocean at a minimum depth of 0 meters (when d = 0) and a maximum depth of 30 meters (when d = 30).
To graph it on a number line, draw a horizontal line and label the points 0 and 30. Then, mark those points on the number line to indicate the minimum and maximum depths where green plants live in the ocean.
Here's what the number line would look like:
-------------|--------|------------------------|---------------
-30 - - 15 0 15 30
The leftmost point (-30) represents depths below the minimum, where green plants cannot survive. The middle point (0) represents the minimum depth at which green plants can live. The rightmost point (30) represents the maximum depth at which green plants can live.