the weight, in pounds, of a newborn baby t months after birth can be modeled by w. a graph of w is shown…

the weight, in pounds, of a newborn baby t months after birth can be modeled by w. a graph of w is shown below. write an equation for w then state the y - intercept of the graph and determine its interpretation in the context of the problem.

the weight, in pounds, of a newborn baby t months after birth can be modeled by w. a graph of w is shown below. write an equation for w then state the y - intercept of the graph and determine its interpretation in the context of the problem.

Answer

Answer:

Equation: $W = 1.2t+ 10$; $y$-intercept: $(0,10)$; Interpretation: The weight of the baby at birth is 10 pounds.

Explanation:

Step1: Find the slope

The line passes through $(0,10)$ and $(5,16)$. Slope $m=\frac{16 - 10}{5-0}=\frac{6}{5}=1.2$.

Step2: Write the equation

Using slope - intercept form $y = mx + b$ (here $W=mt + b$), with $m = 1.2$ and $b = 10$ (the $y$-intercept), we get $W=1.2t + 10$.

Step3: Identify the $y$-intercept

The line crosses the $y$-axis at $t = 0$. When $t=0$, $W = 10$, so the $y$-intercept is $(0,10)$.

Step4: Interpret the $y$-intercept

In the context of the problem, when $t = 0$ (at birth), the weight of the baby is 10 pounds.