Linear vs. Proportional relationships

2y4life

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Feb 26, 2008
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So I have an exam tomorrow on linear and proportional relationships and I'm going through the study sheet and I'm still confused on the difference between linear and proportional relationships. Can someone explain this to me?

The practice questions that I don't know are (yes...it's very elementary)

- What is the relationship between the length of a square and the area of a square (options are linear, proportional, or neither)?
- What is the relationship between the E and m in the equation E=mc2?
- What is the relationship between the elevation at sea level and an elevator (as if moves from one floor to the next)?

These are just a few of the practice problems and if I can answers these, i should do well on the proportions/linear part of the exam. Thanks ahead of time.
 

tkhunny

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"proportional" is a special case of "linear". For proportional, the constant term is zero (0).
 

wjm11

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- What is the relationship between the length of a square and the area of a square (options are linear, proportional, or neither)?
- What is the relationship between the E and m in the equation E=mc2?
Hello, 2y4life,

When we use the terms linear and proportional, we’re talking about how one thing changes with respect to another. It’s very useful to graph them to see what is going on. If the graph makes a straight line, we say there is a “linear” relationship between the variables. If the graph is curved instead, we explain it as some type of “proportionality.”

For example if you consider the relationship between “the length of a side of a square (s)” to its “area (A)” and graph them (with s on the x-axis and A on the y-axis), you don’t get a straight line. Instead, you get a curve called a parabola. Why? The equation for area is

A = s^2

The exponent, 2, on s is the reason. Therefore, we say “A is proportional to the square of s.”

Now let’s look at E = mc^2. We’re asked to describe the relationship between E and m. We see that there is an exponent of 2 on “c,” but it’s not on either of the variables we’re comparing. “c” is just a constant, and even when we square a constant, the result is still just another constant. So we could rewrite the equation into a more general form and simply say

E = m*(some constant)

If we graphed E vs m, with m on the x-axis and E on the y-axis, the graph would be a straight line. (The slope of the line would be the c^2 constant.) Therefore, the relationship between E and m is “linear.”

Hope that helps.
 

2y4life

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Feb 26, 2008
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Thanks guys. You've been very helpful.
 
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