Jordie is baking brownies, so he turns the oven on. As soon as Jordie 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.
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?
x
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?
x
y
(2, 100)(6, 220)
0
2
4
6
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0
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Time (minutes)
Temperature (°F)
y= mx + b
Slope =
Excellent!
Substitute the slope for m in our equation, or the rate of change of the temperature in degrees.
x
y
(2, 100)(6, 220)
0
2
4
6
8
10
12
14
16
0
20
40
60
80
100
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Time (minutes)
Temperature (°F)
y= mx + b
y=
x+b
Slope = 30
Excellent!
Now, solve for b, or the vertical intercept. You can can substitute the x and y-values for a point on the line into the equation to help you. Solve on paper or use the calculator. Then, enter your answer on Zearn.
x
y
(2, 100)(6, 220)
0
2
4
6
8
10
12
14
16
0
20
40
60
80
100
120
140
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180
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220
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280
300
320
340
360
Time (minutes)
Temperature (°F)
y=30x + b
b=
40
Now we have the equation representing the situation: y = 30x + 40. This equation predicts the temperature of the oven at any given time.