Question

(S.ID.7,8,9) A doctor develops the model y = 26.27x + 7 for the number ofwords a toddler can speak (y) versus the months that have passed sincethey started speaking (x). Interpret what the 26.27 and the 7 means in thecontext of the problem.A. An increase of 26.27 words per month and 7 words spoken initiallyB. An increase of 7 words per month and 26.27 words spoken initially

Answer 1

Given:

The number of words a toddler can speak (y) versus the months that have passed since they started speaking (x) is given by the model

`y=26.27x+7`

Required:

We have to interpret what the 26.27 and the 7 means in the context of the problem.

Step-by-step explanation:

The given model can be compared with an equation of a straight line in slop-intercept form. Comparing the given model with

`y=mx+c`

we get

`m=26.27\text{ and }c=7.`

Hence the slope is 26.27 and the intercept is 7. Since the sloe is 26.27 so there is an increase of 26.27 wors per month. And for the initial value, we put x=0 that is at the start of the first month. Then we get,

`\begin{gathered} y=26.27*0+7 \\ y=7 \end{gathered}`

So the words spoken initially were 7.

Final answer:

Hence the final answer is:

A. An increase of 26.27 words per month and 7 words spoken initially.