Roderick can write the proportional relationship for buying pencils with the equation y=$4x

𝑦
=
$
4
𝑥
. What is the constant of proportionality in this equation?

5 answers

In the equation \( y = 4x \), the constant of proportionality is the coefficient of \( x \), which represents the rate at which \( y \) changes with respect to \( x \). In this case, the constant of proportionality is \( 4 \). This means that for every pencil (if \( x \) represents the number of pencils), the cost \( y \) will be $4 per pencil.

Davin wrote the proportional relationship for buying markers with the equation y=$3x
𝑦
=
$
3
𝑥
. The variable x represents the number of boxes and the variable y represents the price. What are the coordinate points if he bought 3 boxes of markers?

In the equation \( y = 3x \), where \( x \) represents the number of boxes of markers and \( y \) represents the total price in dollars, we can find the coordinate points for \( x = 3 \) (which means Davin bought 3 boxes).

Substituting \( x = 3 \) into the equation:

\[ y = 3(3) = 9 \]

Therefore, when Davin bought 3 boxes of markers, the price \( y \) is $9.

The coordinate point representing this situation would be \( (3, 9) \).

This point means that for 3 boxes of markers, the total price is $9.

Determine which equation has a proportional relationship.
Responses

y=x+3
𝑦
=
𝑥
+
3

y is equal to x plus 3

y=8x
𝑦
=
8
𝑥

y is equal to 8 x

y=2x+1
𝑦
=
2
𝑥
+
1

y is equal to 2 x plus 1

y=4x+2
𝑦
=
4
𝑥
+
2

y is equal to 4 x plus 2
Check answerRemaining

A proportional relationship is defined by an equation of the form \( y = kx \), where \( k \) is the constant of proportionality, and there is no constant term added or subtracted (i.e., the equation passes through the origin \((0, 0)\)).

Let's analyze the given equations:

  1. \( y = x + 3 \): This equation is not proportional because it has a constant term (+3).

  2. \( y = 8x \): This equation is proportional, as it can be written in the form \( y = kx \) (where \( k = 8 \)) and passes through the origin.

  3. \( y = 2x + 1 \): This equation is not proportional because it has a constant term (+1).

  4. \( y = 4x + 2 \): This equation is not proportional because it has a constant term (+2).

Conclusion: The equation that has a proportional relationship is \( y = 8x \).

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