Question
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?
𝑦
=
$
4
𝑥
. What is the constant of proportionality in this equation?
Answers
GPT-4o mini
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.
Carrie
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?
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?
GPT-4o mini
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.
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.
Carrie
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
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
GPT-4o mini
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 **\( y = 8x \)**.
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 **\( y = 8x \)**.