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)
0
2
4
6
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10
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16
0
20
40
60
80
100
120
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160
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220
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360
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
8
10
12
14
16
0
20
40
60
80
100
120
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200
220
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280
300
320
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360
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
120
140
160
180
200
220
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280
300
320
340
360
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
160
180
200
220
240
260
280
300
320
340
360
Time (minutes)
Temperature (°F)
y=30x + b
b=
Good work!
Let’s finish writing our equation to represent the relationship between time and the temperature of the oven. Now that we know the temperature of the oven when Jordie turned it on, substitute the vertical intercept for b in our equation.
x
y
(2, 100)(6, 220)
0
2
4
6
8
10
12
14
16
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
Time (minutes)
Temperature (°F)
y
=
30x + b
y
=
30x +
b
=
40
Excellent!
Let’s use the equation to help us make a prediction. Remember x represents the time in minutes, and y represents the temperature of the oven. What will the temperature of the oven be after 8 minutes? Start by substituting 8 minutes for x in the equation.
y
=
30x
+
40
y
=
30
·
+
40
Nice!
Now, solve for y, the temperature after 8 minutes.
y
=
30x
+
40
y
=
30·8
+
40
y
=
30(8) + 40
y = 240 + 40
y = 280
After 8 minutes, the temperature of the oven will be 280 degrees Fahrenheit.