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 (4, 120) and (14, 340) represent?
x
y
(4, 120)(14, 340)
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Time (minutes)
Temperature (°F)
The point (4, 120) means that after
minutes, the oven’s temperature was
degrees Fahrenheit.
The point (14, 340) means that after
minutes, the oven’s temperature was
degrees Fahrenheit.
Nice!
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
(4, 120)(14, 340)
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Time (minutes)
Temperature (°F)
y= mx + b
Slope =
Nice!
Substitute the slope for m in our equation, or the rate of change of the temperature in degrees.
x
y
(4, 120)(14, 340)
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Time (minutes)
Temperature (°F)
y= mx + b
y=
x+b
Slope = 22
You got it!
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
(4, 120)(14, 340)
0
2
4
6
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20
0
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Time (minutes)
Temperature (°F)
y=22x + 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 Sara turned it on, substitute the vertical intercept for b in our equation.
x
y
(4, 120)(14, 340)
0
2
4
6
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14
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20
0
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Time (minutes)
Temperature (°F)
y
=
22x + b
y
=
22x +
b
=
32
Nice!
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 16 minutes? Start by substituting 16 minutes for x in the equation.
y
=
22x
+
32
y
=
22
·
+
32
Nice!
Now, solve for y, the temperature after 16 minutes.
y
=
22x
+
32
y
=
22·16
+
32
y
=
1 answer
To find the temperature of the oven after 16 minutes, we will use the equation we derived:
\[ y = 22x + 32 \]
Substituting \( x = 16 \):
\[ y = 22 \cdot 16 + 32 \]
Now, let's calculate \( y \):
\[ y = 352 + 32 \] \[ y = 384 \]
Thus, the temperature of the oven after 16 minutes will be 384 degrees Fahrenheit.
