This equation shows the linear relationship between the number of minutes since Micah started heating a pot of water and the temperature of the water. x represents the number of minutes, and y represents the temperature in degrees Celsius.

Question

Let’s compare our predictions to the actual data. We predicted after 6 minutes, the temperature would be 80 degrees. How does this compare to the actual temperature on the graph?
x
y
0
2
4
6
8
10
12
0
20
40
60
80
100
120
140
Number of minutes
Temperature (°C)
y=10x+20

x=6, y=80

x=12, y=140
Our prediction is
the actual data on the graph.

Answer 1

To analyze the prediction compared to the actual data, let's look at the equation provided:

The equation of the linear relationship is \( y = 10x + 20 \).

If we want to determine the actual temperature at \( x = 6 \) and \( x = 12 \):

1. At \( x = 6 \): \[ y = 10(6) + 20 = 60 + 20 = 80 \text{ degrees Celsius} \] So, our prediction for \( x = 6 \) is 80 degrees.

2. At \( x = 12 \): \[ y = 10(12) + 20 = 120 + 20 = 140 \text{ degrees Celsius} \] So for \( x = 12 \), we predict that the temperature is 140 degrees.

Now we need to compare these predictions to the actual data on the graph provided. Since we don’t have the actual graph visible here, you would need to check the actual temperature at \( x = 6 \) on the graph.

You’ll compare the predicted temperature of 80 degrees at \( x = 6 \) with the actual data point shown on the graph.

• If the actual temperature on the graph at \( x = 6 \) is also 80 degrees, then our prediction is accurate.
• If the actual temperature is higher or lower than 80 degrees, then our prediction is incorrect.

The same comparison goes for \( x = 12 \), where we predicted 140 degrees; you'd look at the graph to see if the actual temperature corresponds with that prediction.

Summary:

Our prediction for \( x = 6 \) is accurate if the actual temperature on the graph is 80 degrees, and for \( x = 12 \) is accurate if the actual temperature is 140 degrees. Check the graph to confirm these values.