Abby is baking brownies, so she turns the oven on. As soon as Abby turns the oven on, the oven heats up at a constant rate. Write an equation to represent this situation. Then use the equation to make a prediction.

Question

This graph represents the linear relationship between the time in minutes and the temperature of the oven in degrees Fahrenheit. For each minute, the temperature increases at a constant rate. What do the points (2, 100) and (6, 220) represent?
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y
(2, 100)(6, 220)
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Time (minutes)
Temperature (°F)
The point (2, 100) means that after
minutes, the oven’s temperature was
degrees Fahrenheit.

The point (6, 220) means that after
minutes, the oven’s temperature was
degrees Fahrenheit.
You got it!
Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line? In other words, what is the change in degrees for each minute?
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(2, 100)(6, 220)
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Time (minutes)
Temperature (°F)
y= mx + b

Slope =

Answer 1

To find the slope \( m \) of the line representing the relationship between time in minutes \( x \) and temperature in degrees Fahrenheit \( y \), we can use the two points given: \( (2, 100) \) and \( (6, 220) \).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points:

• \( (x_1, y_1) = (2, 100) \)
• \( (x_2, y_2) = (6, 220) \)

Plugging in these values:

\[ m = \frac{220 - 100}{6 - 2} = \frac{120}{4} = 30 \]

Thus, the slope \( m \) is \( 30 \) degrees Fahrenheit per minute. This means the temperature of the oven increases by \( 30 \) degrees Fahrenheit for each additional minute the oven is on.

Now, let's write the equation of the line in the form \( y = mx + b \). We know \( m = 30 \). We need to find the y-intercept \( b \). We can use one of the points to do this. Let’s use the point \( (2, 100) \).

Plugging \( x = 2 \) and \( y = 100 \) into the equation:

\[ 100 = 30(2) + b \]

Simplifying this:

\[ 100 = 60 + b \]

Subtracting \( 60 \) from both sides:

\[ b = 40 \]

Now we have both \( m \) and \( b \). Therefore, the equation representing the temperature of the oven as a function of time is:

\[ y = 30x + 40 \]

Summary of the Points:

• The point \( (2, 100) \) means that after 2 minutes, the oven's temperature was 100 degrees Fahrenheit.
• The point \( (6, 220) \) means that after 6 minutes, the oven's temperature was 220 degrees Fahrenheit.

Final Information:

• Slope \( m = 30 \) degrees per minute.
• Equation of the line: \( y = 30x + 40 \).