Question

ding initial value using a table
the table to the right displays the weight progress of a puppy at the end of week 4. if the relationship between time and weight is linear, how much did the puppy weigh at birth?
4 16
5 18.5
6 21
7 23.5
○ 5.5 pounds
○ 6 pounds
○ 7.5 pounds
○ 16 pounds

Explanation:

Step1: Find the slope

The slope \( m \) of a linear relationship is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((4, 16)\) and \((5, 18.5)\), we have \( m=\frac{18.5 - 16}{5 - 4}=\frac{2.5}{1}=2.5 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((4, 16)\) and \( m = 2.5 \), we get \( y-16 = 2.5(x - 4) \).

Step3: Find the weight at birth (x = 0)

Substitute \( x = 0 \) into the equation: \( y-16=2.5(0 - 4) \). First, calculate \( 2.5\times(- 4)=- 10 \). Then, \( y-16=-10 \). Add 16 to both sides: \( y=16 - 10=6 \).

Answer:

6 pounds