Question

Linear Models

Answer 1

Here you need an explanation.
A linear equation must have the following:
1. Any variable that appears cannot be multiplied by any other variable.
2. No variable may be raised to an exponent.
3. No variable can be an exponent.
4. No variable can be in a denominator.
5. No variable can be in a root or logarithm.
6. Any variable must appear by itself in a term, or at most, multiplied by a number.

Answer 2

okay

Answer 3

For each of the 4 equations you are given, go through the checklist above.

Answer 4

Let's start with A.

\(D=\dfrac{v^2}{15.7}\)

Go through the checklist. Do you see a problem with it?

Answer 5

its being multiplied?

Answer 6

1.

Answer 7

Correct.
\(v^2\) mean v * v
The variable v is being multiplied by a variable (which happens to also be v). That cannot be linear.

Answer 8

B. What about this one?
\(y = 154,000(1.04)^x\)

Answer 9

2. no variable can be an exponent

Answer 10

Exactly. Not linear.
\(y = 154,000(1.04)^\color{red}{x}\)

Answer 11

C. How about this one?

\(B = 1400 + 120m\)

Answer 12

it is linear

Answer 13

Correct.
The term 1400 is just a number with no variables, so there are no problems there.
The term 120m is simply one single variable multiplied by a number, 120, so no problems there either.

Answer 14

D. What about this one?

\(w = 32m\)

Answer 15

it is linear

Answer 16

Correct.
It is similar to C only simpler because it doesn't have the term that is a plain number.
The variable m is just being multiplied by the number 32.

Answer 17

Great job!
You got them all correct.

Answer 18

thanks a ton!! i totally understand now. you rock. have a great day. @mathstudent55 bye! :)

Answer 19

You're welcome.
Thanks.