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To solve this problem, we need to find the equation of the line \( y = mx + b \) that describes the baby's weight over time, where:

- \( x \) is the age of the baby in months.
- \( y \) is the weight of the baby in pounds.
- \( m \) is the rate of change (slope).
- \( b \) is the initial value (y-intercept).

### Step 1: Determine the slope (\( m \))
The problem states that the baby gains 5 pounds every 4 months. Therefore, the slope (\( m \)) is:
\[
m = \frac{\text{change in weight}}{\text{change in age}} = \frac{5 \text{ pounds}}{4 \text{ months}} = \frac{5}{4}
\]

### Step 2: Find the y-intercept (\( b \))
The baby is born with a weight of 6 pounds, which means at \( x = 0 \), \( y = 6 \). Thus, the y-intercept (\( b \)) is 6.

### Step 3: Write the equation
Substitute \( m \) and \( b \) into the equation \( y = mx + b \):
\[
y = \frac{5}{4}x + 6
\]

So, the equation that describes the baby's weight is:
\[
y = \frac{5}{4}x + 6
\]

Would you like more details or have any other questions about this? 

Here are some related questions you might consider:
1. How do you interpret the slope of the line in real-life terms?
2. What would be the baby's weight at 8 months using this equation?
3. How do you graph the equation of this line?
4. How does the equation change if the rate of weight gain changes?
5. What if the baby’s initial weight was different—how would that affect the y-intercept?

**Tip:** The slope represents the rate of change. In word problems, understanding the units (e.g., pounds per month) can help you identify the slope.

A mother gives birth to a 6-pound baby. Every 4 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.

Learn how to find the equation of a line that describes the weight of a baby who gains 5 pounds every 4 months. This problem explores concepts of slope-intercept form and is suitable for students in Grades 6-8.

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