P = 23 + 10(h - 1) People start waiting in line for the release of the newest cell phone at 5 a.m. The equation gives the number of people, P, in line between the hours, h, of 6 a.m. and 11 a.m., when the doors open. Assume that 6 a.m. is when time h = 1. What does the 23 mean in the equation?

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Understand the Context: Understand the context of the problem. The equation P = 23 + 10(h - 1) describes the number of people, P, in line for a cell phone release from 6 a.m. to 11 a.m. We need to determine what the constant 23 represents in this equation.Analyze the Equation: Analyze the equation. The equation is in the form P = a + b(h - c), where a, b, and c are constants. In this context, h represents the number of hours after 6 a.m., and P is the total number of people in line.Identify the Constant: Identify the constant 23. The constant 23 is added to the product of 10 and (h - 1). Since h starts at 1 (which corresponds to 6 a.m.), if we plug h = 1 into the equation, we get P = 23 + 10(1 - 1) = 23 + 10(0) = 23 + 0 = 23.Interpret the Constant: Interpret the constant 23. The calculation in Step 3 shows that when h = 1 (6 a.m.), the number of people in line is 23. This means that the constant 23 represents the initial number of people in line at 6 a.m., before any additional people join the line each hour.

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