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3 years ago

Which graph shows a proportional relationship?

Mathematics

2 answers:

Tasya [4]3 years ago

8 0

Answer: The first one is the proportion

Step-by-step explanation: the reason is because it starts at the orgin.

Verdich [7]3 years ago

6 0

Answer: The only graph that shows a proportional relationship is the line that crosses the origin point (0,0).

Explanation

The other graphs are linear functions but not not proportional relationships.

The general form of a proportional relationship is y = kx, where k is the proportionality constant. So, for x = 0 you will always obtain y = 0.

The general form of a linear relationshio is y = kx + b, being b the y-intercept, so if the y-intercept is not 0, it is not a proportional relationship. That is what happens with the other three graphs.

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Method 1
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Since the numerators are the same, the smaller the denominators, the greater the fraction is.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

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Method 2
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Lets change all to the same denominators

$\dfrac{2}{4} = \dfrac{2 \times 3}{4 \times 3} = \dfrac{6}{12}$

$\dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}$

$\dfrac{2}{6} = \dfrac{2 \times 2}{6 \times 2} = \dfrac{4}{12}$

Now that all the denominators are the same, we can arrange the fractions by comparing the numerators. The bigger the numerators, the greater the fraction.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

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Answer:

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