Write a Linear Model For this Data

[nycmathguy]

Homework Statement

Write a linear model for the given data.

Relevant Equations

y = mx + b

The average weight of a male child’s
brain is 970 grams at age 1 and 1270 grams at age 3. (Source: American Neurological Association)

(a) Assuming that the relationship between brain weight y and age t is linear, write a linear model for the data.

(b) What is the slope and what does it tell you about brain weight?

For (a), I see 2 points in the form (t, y) = (age, weight). The two points are (1, 970) and (3, 1270).

The general form is y = mt + b.

Let m = slope

m = (1270 - 970)/(3 - 1)

m = 300/2

m = 150

I think the point-slope formula needed now.

y - 970 = 150(t - 1)

y - 970 = 150t - 150

y = 150t - 150 + 970

y = 150t + 820

You say?

For (b), the slope is 150. I don't know what the slope tells me about weight gain.

Do you know?

 

[Delta2]

Think about how much the brain weight is increasing every year that passes. (according to the linear model).

 

[nycmathguy]

Think about how much the brain weight is increasing every year that passes. (according to the linear model).

The brain weight increases 150 grams per age.

Yes?

 

[Delta2]

what exactly you mean per age? You mean per year right?

 

[Mark44]

y = 150t + 820

You say?

Can't you check this for yourself? If t = 1, what is y? If t = 3, what is y? Do these y values match the data given in the problem? If so, your equation is correct and you don't need us to confirm your solution.

Homework Statement:: Write a linear model for the given data.
Relevant Equations:: y = mx + b

For (b), the slope is 150. I don't know what the slope tells me about weight gain.

The slope is the rise over the run, which in this case is the change in brain weight (in grams) over the change in time (in years). The units of the slope here are $\frac{\text{grams}}{\text{years}}$, or grams per year.

 

[nycmathguy]

I am moving on. Sorry but I am tired of the belittling. I have not learned anything here. Sorry that I don't recall material learned 28 years ago. I am done! Good night.

 

[nycmathguy]

Delta2,

You are welcomed to join me in my new precalculus FB group.