Math

QuestionWhich equations have the same constant of proportionality as y=12xy=\frac{1}{2} x? Choose 3: A 6y=3x6 y=3 x B C: xx and yy pairs: (4,2), (5,2.5), (10,5)

Studdy Solution

STEP 1

Assumptions1. The equation y=1xy=\frac{1}{} x has a constant of proportionality of 1\frac{1}{}. . We are looking for relationships where the constant of proportionality between yy and xx is also 1\frac{1}{}.

STEP 2

To find the constant of proportionality in the equation 6y=x6y=x, we need to rearrange the equation to the form y=kxy=kx, where kk is the constant of proportionality.
6y=xy=x66y=x \Rightarrow y=\frac{x}{6}

STEP 3

implify the equation to find the constant of proportionality.
y=3x6y=12xy=\frac{3x}{6} \Rightarrow y=\frac{1}{2}x

STEP 4

The constant of proportionality in the equation y=12xy=\frac{1}{2}x is 12\frac{1}{2}, which is the same as in the original equation. So, option A is a correct answer.

STEP 5

Now, let's look at the table. The constant of proportionality in a table can be found by dividing the yy-value by the corresponding xx-value. We need to check if this ratio is the same for all pairs of xx and yy in the table.

STEP 6

Calculate the ratio for the first pair of values in the table.
yx=24=12\frac{y}{x}=\frac{2}{4}=\frac{1}{2}

STEP 7

Calculate the ratio for the second pair of values in the table.
yx=2.55=12\frac{y}{x}=\frac{2.5}{5}=\frac{1}{2}

STEP 8

Calculate the ratio for the third pair of values in the table.
yx=510=12\frac{y}{x}=\frac{5}{10}=\frac{1}{2}

STEP 9

The ratio yx\frac{y}{x} is the same for all pairs of values in the table and equals 2\frac{}{2}, which is the same as in the original equation. So, option C is also a correct answer.
Based on the above steps, the relationships that have the same constant of proportionality between yy and xx as the equation y=2xy=\frac{}{2} x are options A and C.

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