Determine whether each equation represents a proportional relationship. If it does, identify the constant of proportionality. a. y = 0.5x - 2 b. y = 1,000x c. y = x + 1

Tammy Todd

Tammy Todd

Answered question

2021-02-02

Determine whether each equation represents a proportional relationship. If it does, identify the constant of proportionality. a.y=0.5x2
b.y=1,000x
c.y=x+1

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-02-03Added 109 answers

An equation has a proportional relationship if it can be written in the form y=kx where k is the constant of proportionality.
a.y=0.5x2 does not have a proportional relationship since it has the term −2 on the right side.
b.y=1,000x has a proportional relationship with a constant of proportionality of 1,000.
c.y=x+1 does not have a proportional relationship since it has the term 1 on the right side.
Jazz Frenia

Jazz Frenia

Skilled2023-05-23Added 106 answers

Result:
a) Equation y=0.5x2 does represent a proportional relationship with a constant of proportionality k=0.5.
b) Equation y=1000x represents a proportional relationship with a constant of proportionality k=1000.
c) Equation y=x+1 does not represent a proportional relationship.
Solution:
a) Equation: y=0.5x2
To determine if this equation represents a proportional relationship, we can rewrite it in the form y=kx.
0.5x2=kx
Rearranging the terms:
0.5xkx=2
Factoring out the common factor of x:
x(0.5k)=2
For this equation to hold true for all values of x, the expression in the parentheses, (0.5k), must be equal to zero. Therefore, k=0.5 for this equation to represent a proportional relationship.
b) Equation: y=1000x
This equation is already in the form y=kx. The constant of proportionality is k=1000.
c) Equation: y=x+1
Similar to the previous equation, this equation is not in the form y=kx. The presence of the constant term 1 on the right side indicates that it does not represent a proportional relationship.
Andre BalkonE

Andre BalkonE

Skilled2023-05-23Added 110 answers

We may compare the supplied equations to the general form of a proportional connection, which is y=kx, where k denotes the constant of proportionality, to determine whether each equation reflects a proportional relationship and to find the constant of proportionality.
a) The equation y=0.5x2 does not represent a proportional relationship because the coefficient of x is not a constant. It is 0.5, which means the ratio between y and x is not constant. Hence, we cannot identify a constant of proportionality for this equation.
b) The equation y=1,000x represents a proportional relationship. The coefficient of x is a constant, which is 1,000. Therefore, the constant of proportionality for this equation is 1,000.
c) The equation y=x+1 does not represent a proportional relationship because it is in the form of a linear equation with a constant term (1) added to x. In a proportional relationship, there should not be a constant term added or subtracted. Therefore, we cannot identify a constant of proportionality for this equation.
Answer:
a) y=0.5x2 does not represent a proportional relationship. No constant of proportionality.
b) y=1,000x represents a proportional relationship with a constant of proportionality of 1,000.
c) y=x+1 does not represent a proportional relationship. No constant of proportionality.

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