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Graphs - Proportional Relationship

What is a "proportional relationship" ?

(other common terms which mean the same thing: “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable with "proportional relationship".)

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May 03, 2011
Graphs - Proportional Relationship
by: Staff

The question:

what is a proportional relationship

The answer:

In mathematics, the terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

The equation for a “proportional relationship” ALWAYS looks like this:

y = kx

k is a constant. It is called the “constant of variation”.

[a “proportional relationship” can also be written as the function: f(x) = kx]

y = kx is a special case of the linear equation y = kx + b, where b = 0

Note that a “proportional relationship” (y = kx) and a “linear relationship” (y = kx + b) are not the same. A “proportional relationship” is more restrictive than a “linear relationship”.

All of us use proportional relationships to calculate cause and effect.

For example, if you are driving a car at 50 mph, how far will you travel in 3 hours?

The answer is:

y = kx

y = distance

k = 50 mph

x = time = 3 hours

distance in miles = (50 mph)*(time in hours)

distance = 50 mph * 3 hours = 150 miles

Now suppose you want to know how far you will travel in 4 ½ hours.

The equation is the same:

The answer is:

distance in miles = (50 mph)*(time in hours)

k = 50 mph

x = time = 4 ½ hours

distance = 50 mph * 4 ½ hours = 225 miles.

To plot the proportional relationship in the example, (1) make a table of values, and then (2) plot the values in the table.

Table of Values for the Equation:

distance in miles = (50 mph)*(time in hours)

time in hours, distance traveled in miles

0, 0
1, 50
2, 100
3, 150
4, 200

When these points are plotted, the result is a straight line which begins at 0 and has a positive slope. (The graph of a “proportional relationship” always passes through the origin: 0,0.)

distance in miles = (50 mph)*(time in hours).

To view this graph, click the following link, or (1) highlight and copy the link, then (2) paste the link into your browser Address Bar & press enter):

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Thanks for writing.


Jun 05, 2020
answer NEW
by: Anonymous

Does this represent a proportional relationship? Explain your answer. A salad dressing calls for 3 parts oil and 1 part vinegar. Manuela uses 2 tablespoons of vinegar and 6 tablespoons of oil to make her salad dressing.

Oct 13, 2020
Linear Proportional Relationships NEW
by: Anonymous


Nov 16, 2020
Are they proportional NEW
by: Anonymous

(4,36) ( 13, 117 )

May 17, 2021
are these proportional
by: Anonymous

x y x y x y

0 0 0 1 3 8
1 3 4 2 3.75 10

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