Question

For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 1 minute of play, the game awards one half point, and for every 7 minutes of play, the game awards three and one half points.

Part A: Find the constant of proportionality. Show every step of your work. (4 points)

Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)

Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)

Part D: How many points are awarded for 18 minutes of play? (2 points)

I am running low on funds. Please respond quickly as this is time-sensitive.s is time-sensitive.

Answer 1

Answer: Part A: 1/2 Part B: (1/2)x

Step-by-step explanation: Part A: To find the constant of proportionality, set up a proportion using the given information. Let "x" represent the number of minutes played and "y" represent the number of points awarded. Using the data points, we can set up the proportion as (1 minute of play) / (1/2 point) = (7 minutes of play) / (3 1/2 points). Cross-multiply and simplify to find that the constant of proportionality is 1/2.

Part B: The equation that represents the relationship between minutes played (x) and points awarded (y) is y = (1/2)x.

Answer 2

Part A:

To find the constant of proportionality, we can use the information provided. For every 1 minute of play, the game awards one half point. We can set up a proportion to find the constant.

Let x represent the time played in minutes, and let y represent the points awarded.

We can write the proportion as:

1 minute / 0.5 points = x minutes / y points

Simplifying the proportion, we have:

1 / 0.5 = x / y

2 = x / y

Cross-multiplying, we get:

2y = x

So, the constant of proportionality is 2.

Part B:

To write an equation that represents the relationship, we can use the constant of proportionality. Since the number of points awarded is proportional to the time played, we can express it as:

y = kx

Where y represents the points awarded, x represents the time played in minutes, and k represents the constant of proportionality. Substituting the value of k, we have:

y = 2x

Part C:

To graph the relationship, we can plot points on a coordinate plane using the equation y = 2x. The x-axis represents the time played, and the y-axis represents the points awarded. We can choose different values for x (time played) and calculate the corresponding y (points awarded) using the equation.

For example, if we choose x = 1, we have y = 2(1) = 2. This means that 1 minute of play corresponds to 2 points.

Similarly, if we choose x = 7, we have y = 2(7) = 14. This means that 7 minutes of play corresponds to 14 points.

By plotting these points and connecting them with a line, we can graphically represent the relationship between time played and points awarded.

Part D:

To find the number of points awarded for 18 minutes of play, we can use the equation y = 2x. Plugging in x = 18, we have:

y = 2(18) = 36

Therefore, for 18 minutes of play, the game awards 36 points.

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