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The weight, in pounds, of a newborn baby t months after birth can be modeled by W . Th table below has select values showing the linear relationship between t and W . Determin the number of pounds the baby gains per month. t & W 5 & 12.25 7 & 14.75 9 & 17.25

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The weight, in pounds, of a newborn baby t months after birth can be modeled by W . Th table below has select values showing the linear relationship between t and W . Determin the number of pounds the baby gains per month.

 t & W 
 5 & 12.25 
 7 & 14.75 
 9 & 17.25

The weight, in pounds, of a newborn baby t months after birth can be modeled by W . Th table below has select values showing the linear relationship between t and W . Determin the number of pounds the baby gains per month. t & W 5 & 12.25 7 & 14.75 9 & 17.25

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EmersonVeteran · Tutor for 11 years

Answer

### The baby gains 1.25 pounds per month.

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## Step 1: Identify the linear relationship<br />### The relationship between \( t \) and \( W \) is linear, meaning it can be represented by the equation \( W = mt + b \), where \( m \) is the slope (rate of weight gain per month) and \( b \) is the y-intercept.<br />## Step 2: Calculate the slope \( m \)<br />### The slope \( m \) is calculated using the formula \( m = \frac{\Delta W}{\Delta t} \). Using the given points, we can calculate the slope between any two points. For example, between \( t = 5 \) and \( t = 7 \):<br />\[ m = \frac{W(7) - W(5)}{7 - 5} = \frac{14.75 - 12.25}{2} = \frac{2.5}{2} = 1.25 \]<br />## Step 3: Verify the slope with another pair of points<br />### To ensure consistency, we can verify the slope using another pair of points, such as \( t = 7 \) and \( t = 9 \):<br />\[ m = \frac{W(9) - W(7)}{9 - 7} = \frac{17.25 - 14.75}{2} = \frac{2.5}{2} = 1.25 \]<br />### The slope is consistent across different pairs of points, confirming that the baby gains 1.25 pounds per month.
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