The temperature at sunrise is 36degreesF. Each​ hour, the temperature rises 6degreesF. Write an equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours. What is the graph of the​ equation?

Question

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Part 1
Write an equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours.
  
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​(Type an equation. Simplify your answer. Type your answer in​ slope-intercept form.)

Answer 1

To model the temperature \( y \) in degrees Fahrenheit after \( x \) hours, we start with the information given:

• The initial temperature at sunrise (when \( x = 0 \)) is 36 degrees F.
• The temperature rises by 6 degrees F each hour.

Using the slope-intercept form of a linear equation, which is \( y = mx + b \):

• \( b \) is the initial value (the y-intercept), which is 36 degrees.
• \( m \) is the rate of change, which is 6 degrees per hour.

Thus, the equation that models the temperature \( y \) after \( x \) hours is:

\[ y = 6x + 36 \]

Part 2: Graph of the Equation

To graph the equation \( y = 6x + 36 \):

1. Identify the y-intercept: The y-intercept is 36 (this is where the line crosses the y-axis when \( x = 0 \)).

2. Find another point using the slope: The slope is 6, meaning for every 1 hour increase (1 unit increase in \( x \)), \( y \) increases by 6 degrees F.

   • For \( x = 1 \): \[ y = 6(1) + 36 = 6 + 36 = 42 \]
   • So, the point (1, 42) can also be plotted.

3. Draw the Line: Now you can plot the points (0, 36) and (1, 42) on a graph and draw a straight line through them extending in both directions.

This will give you the graph of the equation \( y = 6x + 36 \). The line will rise steeply due to the slope of 6, indicating a rapid increase in temperature.

Summary

The equation modeling the temperature after \( x \) hours is:

\[ y = 6x + 36 \]