Chapter 7 7.1 Slope-Intercept Form Worksheet - Mhr Page 9
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17Example 4
Determine an Unknown Parameter
Did You Know?
An archaeologist simulates a
To boil water, some First
First Nations method of boiling
Nations people used to
water by adding hot rocks to an
dig a bowl-shaped pit in
earthen pit fi lled with water. As
the ground. Then, they
the rocks cool and lose their heat,
lined the bottom with
buffalo hide. They added
the archaeologist replaces them
water and red-hot rocks
with new rocks from the fi re.
to the pit, until the water
Suppose the water temperature
Cooking in a Fire Pit by Shayne Tolman
boiled.
rises at a constant rate. The
Painting on display at Head-Smashed-In Buffalo
Jump Interpretive Centre likely represents
temperature of the water at the
2500-year-old Besant culture.
start of the experiment is 10 °C.
The equation W = mt + 10 models how the temperature of the
water, W, in degrees Celsius, increases at a constant rate of m
degrees Celsius per minute for t minutes.
After 5 min, the water temperature is 19 °C. Determine the value
a)
of the parameter m. What does m represent?
How long will it take for the water to boil?
b)
Solution
Represent a temperature of 19 °C after 5 min as the point (5, 19).
a)
Did You Know?
Substitute the coordinates of the point (5, 19) into the given
The coordinates of a
equation. Solve for m.
point on a graph satisfy
W = mt + 10
the equation of the
19
= m(5) + 10
graph. Conversely, a
19 - 10 = 5m
point whose coordinates
9 = 5m
satisfy an equation is a
_
9
point on a graph of the
= m or m = 1.8
5
equation.
The parameter m represents the rate at which the temperature of
For example,
the water increases per minute. The water temperature increases
The point (1, 8) is a point
at a rate of 1.8 °C/min.
on the graph of y = 3x + 5.
Substituting x = 1 and
Solve the equation for t when W is 100 °C.
b)
What does W = 100 °C
y = 8.
represent?
W = 1.8t + 10
8
= 3(1) + 5
100
= 1.8t + 10
8 = 8
True.
90 = 1.8t
Conversely, since the
50 = t
point (1, 8) satisfi es
The water boils after 50 min.
the equation, (1, 8) is a
point on the graph of the
Your Turn
equation y = 3x + 5.
A decorator’s fee can be modelled by the equation F = 75t + b. In the
equation, F represents the fee, in dollars, t represents time, in hours,
and b represents the cost of the initial consultation, in dollars.
Suppose the decorator spends 4 h working for a client and
a)
charges the client $450. Determine the value of the parameter b.
How many hours does the decorator work if a client is
b)
charged $975?
348
MHR • Chapter 7
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