Question

question
the weight, in pounds, of a newborn baby ( t ) months after birth can be modeled by ( w = 2t + 11 ). what is the ( y )-intercept of the equation and what is its interpretation in the context of the problem?
answer
attempt 1 out of 2

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In the given equation $W=2t + 11$, we can compare it with the slope - intercept form (here $W$ is like $y$ and $t$ is like $x$).

Step2: Identify the y - intercept

By comparing $W = 2t+11$ with $y=mx + b$, we can see that the coefficient of $t$ (the slope $m$) is 2 and the constant term $b$ (the $y$-intercept) is 11.

Step3: Interpret the y - intercept in context

In the context of the problem, $t$ represents the number of months after birth. When $t = 0$, that corresponds to the time of birth (0 months after birth). Substituting $t = 0$ into the equation $W=2(0)+11$, we get $W = 11$. So the $y$-intercept (which is 11) represents the weight of the newborn baby at birth (when $t = 0$ months), and the weight is 11 pounds.

Answer:

The $y$-intercept of the equation $W = 2t+11$ is 11. In the context of the problem, it means that the weight of the newborn baby at birth (when $t = 0$ months, i.e., at the time of birth) is 11 pounds.