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Joseph Lee
Metropolitan Community College
Joseph Lee
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Definition: Perimeter of a Rectangle
The perimeter of a rectangle is the distance around the edges. The
perimeter is given by
P = 2l + 2w
where l represents the length of the rectangle and w represents the
width of the rectangle.
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
Solution.
P = 2l + 2w
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
Solution.
P = 2l + 2w
26 = 2l + 2(5)
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
Solution.
P = 2l + 2w
26 = 2l + 2(5)
26 = 2l + 10
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
Solution.
P = 2l + 2w
26 = 2l + 2(5)
26 = 2l + 10
16 = 2l
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Example 1.a
Find the length of a rectangle if P = 26 and w = 5.
Solution.
P = 2l + 2w
26 = 2l + 2(5)
26 = 2l + 10
16 = 2l
8= l
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
Solution.
P = 2l + 2w
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
Solution.
P = 2l + 2w
48 = 2l + 2(13)
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
Solution.
P = 2l + 2w
48 = 2l + 2(13)
48 = 2l + 26
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
Solution.
P = 2l + 2w
48 = 2l + 2(13)
48 = 2l + 26
22 = 2l
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Example 1.b
Find the length of a rectangle if P = 48 and w = 13.
Solution.
P = 2l + 2w
48 = 2l + 2(13)
48 = 2l + 26
22 = 2l
11 = l
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Example 1.c
Find the length of any rectangle with perimeter, P, and width, w .
Joseph Lee
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Example 1.c
Find the length of any rectangle with perimeter, P, and width, w .
Solution.
P = 2l + 2w
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Example 1.c
Find the length of any rectangle with perimeter, P, and width, w .
Solution.
P = 2l + 2w
P − 2w = 2l
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Example 1.c
Find the length of any rectangle with perimeter, P, and width, w .
Solution.
P = 2l + 2w
P − 2w = 2l
2l
P − 2w
=
2
2
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Example 1.c
Find the length of any rectangle with perimeter, P, and width, w .
Solution.
P = 2l + 2w
P − 2w = 2l
2l
P − 2w
=
2
2
P − 2w
= l
2
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Definition: Distance Formula
The distance formula calculates the distance traveled by an object
with constant rate. The distance is given by
d = rt
where r represents the rate of the object and t represents the time
traveled at that rate.
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Example 2.a
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 60.
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Example 2.a
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 60.
Solution.
d = rt
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Example 2.a
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 60.
Solution.
d = rt
180 = (60)t
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Example 2.a
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 60.
Solution.
d = rt
180 = (60)t
180
60t
=
60
60
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Example 2.a
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 60.
Solution.
d = rt
180 = (60)t
180
60t
=
60
60
3= t
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Example 2.b
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 50.
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Example 2.b
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 50.
Solution.
d = rt
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Example 2.b
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 50.
Solution.
d = rt
180 = (50)t
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Example 2.b
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 50.
Solution.
d = rt
180 = (50)t
180
50t
=
50
50
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Example 2.b
Find the time traveled by an object that travels for d = 180 at
with a constant rate of r = 50.
Solution.
d = rt
180 = (50)t
180
50t
=
50
50
18
= t
5
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Example 2.c
Find the time traveled by any object that travels any distance, d,
with a constant rate, r .
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Example 2.c
Find the time traveled by any object that travels any distance, d,
with a constant rate, r .
Solution.
d = rt
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Example 2.c
Find the time traveled by any object that travels any distance, d,
with a constant rate, r .
Solution.
d = rt
d
rt
=
r
r
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Example 2.c
Find the time traveled by any object that travels any distance, d,
with a constant rate, r .
Solution.
d = rt
d
rt
=
r
r
d
= t
r
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Definition: Simple Interest
The simple interest on a loan is the interest earned only on the
principal. The simple interest is given by
i = prt
where p represents the amount of principal, r represents the
interest rate as a decimal, and t represents the time, usually
calculated in years.
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
50 = (1000)(r )(2)
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
50 = (1000)(r )(2)
50 = 2000r
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
50 = (1000)(r )(2)
50 = 2000r
50
2000r
=
2000
2000
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
50 = (1000)(r )(2)
50 = 2000r
50
2000r
=
2000
2000
0.025 = r
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Example 3.a
Find the interest rate on a loan of $1000 that earns $50 simple
interest over 2 years.
Solution.
i = prt
50 = (1000)(r )(2)
50 = 2000r
50
2000r
=
2000
2000
0.025 = r
Thus, the interest rate is $2.5%.
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Example 3.b
Find the interest rate on any loan of principal, p, that earns i
simple interest over t years.
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Example 3.b
Find the interest rate on any loan of principal, p, that earns i
simple interest over t years.
Solution.
i = prt
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Example 3.b
Find the interest rate on any loan of principal, p, that earns i
simple interest over t years.
Solution.
i = prt
i
prt
=
pt
pt
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Example 3.b
Find the interest rate on any loan of principal, p, that earns i
simple interest over t years.
Solution.
i = prt
i
prt
=
pt
pt
i
= r
pt
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Definition: Linear Equation in Two Variables
A linear equation in two variables is any equation
Ax + By = C
where A, B, and C are real numbers.
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Definition: Linear Equation in Two Variables
A linear equation in two variables is any equation
Ax + By = C
where A, B, and C are real numbers.
Examples
1
2x + 3y = 6
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Definition: Linear Equation in Two Variables
A linear equation in two variables is any equation
Ax + By = C
where A, B, and C are real numbers.
Examples
1
2x + 3y = 6
2
x − 4y = 8
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Definition: Linear Equation in Two Variables
A linear equation in two variables is any equation
Ax + By = C
where A, B, and C are real numbers.
Examples
1
2x + 3y = 6
2
x − 4y = 8
A linear equation in two variables may be written in y = mx + b
form.
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Example 4.a
Write 2x + 3y = 6 in y = mx + b form.
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Example 4.a
Write 2x + 3y = 6 in y = mx + b form.
Solution.
2x + 3y = 6
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Example 4.a
Write 2x + 3y = 6 in y = mx + b form.
Solution.
2x + 3y = 6
3y = −2x + 6
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Example 4.a
Write 2x + 3y = 6 in y = mx + b form.
Solution.
2x + 3y = 6
3y = −2x + 6
1
1
(3y ) = (−2x + 6)
3
3
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Example 4.a
Write 2x + 3y = 6 in y = mx + b form.
Solution.
2x + 3y = 6
3y = −2x + 6
1
1
(3y ) = (−2x + 6)
3
3
2
y = − x +2
3
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Example 4.b
Write x − 4y = 8 in y = mx + b form.
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Example 4.b
Write x − 4y = 8 in y = mx + b form.
Solution.
x − 4y = 8
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Example 4.b
Write x − 4y = 8 in y = mx + b form.
Solution.
x − 4y = 8
−4y = −x + 8
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Example 4.b
Write x − 4y = 8 in y = mx + b form.
Solution.
x − 4y = 8
−4y = −x + 8
1
1
− (−4y ) = − (−x + 8)
4
4
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Example 4.b
Write x − 4y = 8 in y = mx + b form.
Solution.
x − 4y = 8
−4y = −x + 8
1
1
− (−4y ) = − (−x + 8)
4
4
y=
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1
x −2
4
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Example 4.c
Write y + 2 = −3(x − 1) in y = mx + b form.
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Example 4.c
Write y + 2 = −3(x − 1) in y = mx + b form.
Solution.
y + 2 = −3(x − 1)
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Example 4.c
Write y + 2 = −3(x − 1) in y = mx + b form.
Solution.
y + 2 = −3(x − 1)
y + 2 = −3x + 3
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Example 4.c
Write y + 2 = −3(x − 1) in y = mx + b form.
Solution.
y + 2 = −3(x − 1)
y + 2 = −3x + 3
y = −3x + 1
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Example 4.d
Write 3x − 5y + 2 = 0 in y = mx + b form.
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Example 4.d
Write 3x − 5y + 2 = 0 in y = mx + b form.
Solution.
3x − 5y + 2 = 0
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Example 4.d
Write 3x − 5y + 2 = 0 in y = mx + b form.
Solution.
3x − 5y + 2 = 0
−5y = −3x − 2
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Example 4.d
Write 3x − 5y + 2 = 0 in y = mx + b form.
Solution.
3x − 5y + 2 = 0
−5y = −3x − 2
1
1
− (−5y ) = − (−3x − 2)
5
5
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Example 4.d
Write 3x − 5y + 2 = 0 in y = mx + b form.
Solution.
3x − 5y + 2 = 0
−5y = −3x − 2
1
1
− (−5y ) = − (−3x − 2)
5
5
y=
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3
2
x+
5
5
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