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Tanzania [10]
3 years ago
15

Which equation represents a proportional relationship? A. y = x + 1 3 y=x+13 B. y = 1 − 1 3 x y=1-13x C. y = 3 x + 1 3 y=3x+13 D

. y = 1 3 x
Mathematics
1 answer:
34kurt3 years ago
3 0

Answer:

Option D. y=\frac{1}{3}x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

case A) we have

y=x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=0+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation A not represent a proportional relationship

case B) we have

y=1-\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=1-\frac{1}{3}(0)=1

so

The line not passes through the origin

therefore

The equation B not represent a proportional relationship

case C) we have

y=3x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=3(0)+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation C not represent a proportional relationship

case D) we have

y=\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=\frac{1}{3}(0)=0

so

The line passes through the origin

therefore

The equation D represent a proportional relationship

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