HyperSniper445
  • HyperSniper445
Linear Models
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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HyperSniper445
  • HyperSniper445
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mathstudent55
  • mathstudent55
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.
HyperSniper445
  • HyperSniper445
okay

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mathstudent55
  • mathstudent55
For each of the 4 equations you are given, go through the checklist above.
mathstudent55
  • mathstudent55
Let's start with A. \(D=\dfrac{v^2}{15.7}\) Go through the checklist. Do you see a problem with it?
HyperSniper445
  • HyperSniper445
its being multiplied?
HyperSniper445
  • HyperSniper445
1.
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
B. What about this one? \(y = 154,000(1.04)^x\)
HyperSniper445
  • HyperSniper445
2. no variable can be an exponent
mathstudent55
  • mathstudent55
Exactly. Not linear. \(y = 154,000(1.04)^\color{red}{x}\)
mathstudent55
  • mathstudent55
C. How about this one? \(B = 1400 + 120m\)
HyperSniper445
  • HyperSniper445
it is linear
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
D. What about this one? \(w = 32m\)
HyperSniper445
  • HyperSniper445
it is linear
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
Great job! You got them all correct.
HyperSniper445
  • HyperSniper445
thanks a ton!! i totally understand now. you rock. have a great day. @mathstudent55 bye! :)
mathstudent55
  • mathstudent55
You're welcome. Thanks.

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