2.4 Write Equations Of Lines Examples And Worksheet - Chapter 2, Linear Equations And Functions Page 3
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1
2
3
4
5
6
7
8
9E
4
Write an equation given two points
X A M P L E
Write an equation of the line that passes through (5, 22) and (2, 10).
ANOTHER WAY
Solution
For an alternative
The line passes through (x
, y
) 5 (5, 22) and (x
, y
) 5 (2, 10). Find its slope.
1
1
2
2
method for solving the
y
2 y
problem in Example 4,
10 2 (22)
12
2
1
m 5
5
5
5 24
}
}
}
x
2 x
turn to page 105 for
2 2 5
23
2
1
the
Problem Solving
You know the slope and a point on the line, so use point-slope form with either
Workshop.
given point to write an equation of the line. Choose (x
, y
) 5 (2, 10).
1
1
y 2
y
5 m(x 2
x
)
Use point-slope form.
1
1
y 2
10
5 24(x 2 2)
Substitute for m, x
, and y
.
1
1
y 2 10 5 24x 1 8
Distributive property
y 5 24x 1 18
Write in slope-intercept form.
E
5
Write a model using slope-intercept form
X A M P L E
SPORTS
In the school year ending in 1993, 2.00 million
females participated in U.S. high school sports. By 2003,
the number had increased to 2.86 million. Write a linear
equation that models female sports participation.
Solution
Define
STEP 1
the variables. Let x represent the time
(in years) since 1993 and let y represent the
number of participants (in millions).
Identify
the initial value and rate of change. The
STEP 2
initial value is 2.00. The rate of change is the slope m.
y
2 y
5
Use (x
, y
)
(0, 2.00)
AVOID ERRORS
2.86 2 2.00
0.86
2
1
1
1
m 5
5 0.086
5
5
}
}
}
x
2 x
and (x
, y
)
5
(10, 2.86).
10 2 0
10
Because time is
2
1
2
2
defi ned in years since
STEP 3
Write
a verbal model. Then write a linear equation.
1993 in Step 1, 1993
corresponds to x
5 0
Participants
Initial
Rate of
Years
1
p
5
1
and 2003 corresponds
number
change
since 1993
(millions)
to x
5 10.
2
p
y
2.00
0.086
x
5
1
c
In slope-intercept form, a linear model is y 5 0.086x 1 2.00.
✓
G
P
for Examples 4 and 5
UIDED
RACTICE
Write an equation of the line that passes through the given points.
(22, 5), (4, 27)
(6, 1), (23, 28)
(21, 2), (10, 0)
6.
7.
8.
SPORTS
In Example 5, the corresponding data for males are 3.42 million
9.
participants in 1993 and 3.99 million participants in 2003. Write a linear
equation that models male participation in U.S. high school sports.
100
Chapter 2 Linear Equations and Functions
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