A baby was born with a weight of 12 pounds and then began to gain weight at a constant rate. After 6 months, the baby's weight was 24 pounds. Write an equation for W, commaW, in terms of t, commat, representing weight, in pounds, of the newborn baby tt months after birth.

We are given that the baby was born weighing 12 pounds and gained weight at a constant rate, reaching 24 pounds after 6 months. To write an equation for the baby’s weight \(W(t)\) as a function of time \(t\) (in months), let’s follow these steps:

### Step 1: Identify key information.
- **Initial weight** at \(t = 0\): \(W(0) = 12\) pounds.
- **Weight at \(t = 6\)** months: \(W(6) = 24\) pounds.
- The baby gains weight **linearly** with time, meaning we can use the equation of a line:  
  \[ W(t) = mt + b \]  
  where \(m\) is the slope (rate of weight gain) and \(b\) is the initial weight.

### Step 2: Calculate the slope \(m\).
The slope \(m\) is the rate of change of weight over time. Using the given points \((0, 12)\) and \((6, 24)\):
\[
m = \frac{24 - 12}{6 - 0} = \frac{12}{6} = 2 \, \text{pounds per month}.
\]
This tells us the baby gains 2 pounds per month.

### Step 3: Write the equation.
Since the baby weighed 12 pounds at birth (\(b = 12\)), the equation becomes:
\[
W(t) = 2t + 12.
\]

### Step 4: Final equation.
The equation representing the baby’s weight \(W\), in pounds, at \(t\) months after birth is:
\[
W(t) = 2t + 12.
\]

Would you like to see more details or examples on how to use this equation?  

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### Related Questions:
1. What will be the baby’s weight after 9 months?
2. How many months will it take for the baby to weigh 30 pounds?
3. What does the slope \(m\) represent in this problem?
4. If the rate of weight gain was 3 pounds per month, how would the equation change?
5. What is the domain and range of the function \(W(t) = 2t + 12\) for the first year?

**Tip:** When working with linear equations, always identify the slope as the rate of change and the intercept as the starting value.

A baby was born with a weight of 12 pounds and then began to gain weight at a constant rate. After 6 months, the baby's weight was 24 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.

Learn how to write a linear equation representing a baby's weight gain over time. This problem involves calculating the rate of change and using the slope-intercept form to model the situation. The baby was born weighing 12 pounds and gained 2 pounds per month, reaching 24 pounds after 6 months. Suitable for Grades 6-8.

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