Math Problem Statement

Which equation has a constant of proportionality equal to [10]? Choose 1 answer: Choose 1 answer: (Choice A)

[y=\dfrac{2}{20}x] A

[y=\dfrac{2}{20}x] (Choice B)

[y=\dfrac{30}{3}x] B

[y=\dfrac{30}{3}x] (Choice C)

[y=\dfrac{12}{2}x] C

[y=\dfrac{12}{2}x] (Choice D)

[y=\dfrac{5}{5}x] D

[y=\dfrac{5}{5}x]

Solution

To determine which equation has a constant of proportionality equal to 10, we need to identify the coefficient of xx in each equation, as the general form for a direct variation is y=kxy = kx, where kk is the constant of proportionality.

Let's evaluate each choice:

  1. Choice A:
    y=220x=110xy = \frac{2}{20}x = \frac{1}{10}x
    Constant of proportionality k=110k = \frac{1}{10}.

  2. Choice B:
    y=303x=10xy = \frac{30}{3}x = 10x
    Constant of proportionality k=10k = 10.

  3. Choice C:
    y=122x=6xy = \frac{12}{2}x = 6x
    Constant of proportionality k=6k = 6.

  4. Choice D:
    y=55x=1xy = \frac{5}{5}x = 1x
    Constant of proportionality k=1k = 1.

The only equation with a constant of proportionality equal to 10 is Choice B:
y=303xy = \frac{30}{3}x

Would you like further details or explanations? Here are some related questions you might consider:

  1. What does the constant of proportionality represent in a linear equation?
  2. How do you convert a fraction into a decimal?
  3. Can you explain how to identify constants of proportionality in other forms of equations?
  4. What are some real-world applications of proportional relationships?
  5. How does changing the constant of proportionality affect the graph of the equation?

Tip: Always check the coefficient of xx in the equation to quickly determine the constant of proportionality.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Proportional Relationships

Formulas

y = kx

Theorems

-

Suitable Grade Level

Grades 6-8