Post on 08-Jan-2018
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UNIT 2, LESSON 8
VARIATION
THREE TYPES OF VARIATION
D ire c t In verse C om b in ed
V a ria tion
CONSTANT OF VARIATION
•Represented by the letter “k”.
DIRECT VARIATION
• y=kx
DIRECT VARIATION
• Find an equation of variation where y varies directly as the square of x, and y=12 when x=2.
DIRECT VARIATION
• Find an equation of variation where y varies directly as the square of x, and y=12 when x=2.
2kxy
DIRECT VARIATION
• Find an equation of variation where y varies directly as the square of x, and y=12 when x=2.
2kxy 2212 k
DIRECT VARIATION
• Find an equation of variation where y varies directly as the square of x, and y=12 when x=2.
2kxy 2212 kk3
DIRECT VARIATION
• Find an equation of variation where y varies directly as the square of x, and y=12 when x=2.
2kxy 2212 kk3
23xy
INVERSE VARIATION• y=k / x
INVERSE VARIATION• Find an equation of
variation where y varies inversely as the square of x, and y=3 when x=5.
INVERSE VARIATION• Find an equation of
variation where y varies inversely as the square of x, and y=3 when x=5.
2xky
INVERSE VARIATION• Find an equation of
variation where y varies inversely as the square of x, and y=3 when x=5.
2xky
253 k
INVERSE VARIATION• Find an equation of
variation where y varies inversely as the square of x, and y=3 when x=5.
2xky
253 k
k75
INVERSE VARIATION• Find an equation of
variation where y varies inversely as the square of x, and y=3 when x=5.
2xky
253 k
k75 2
75x
y
COMBINED VARIATION• y=kxz
COMBINED VARIATION• Find an equation of
variation where y varies jointly as x and z, and y=42 when x=2 and z=3.
COMBINED VARIATION• Find an equation of
variation where y varies jointly as x and z, and y=42 when x=2 and z=3.
kxzy
COMBINED VARIATION• Find an equation of
variation where y varies jointly as x and z, and y=42 when x=2 and z=3.
kxzy 3242 k
COMBINED VARIATION• Find an equation of
variation where y varies jointly as x and z, and y=42 when x=2 and z=3.
kxzy 3242 kk7
COMBINED VARIATION• Find an equation of
variation where y varies jointly as x and z, and y=42 when x=2 and z=3.
kxzy 3242 kk7xzy 7
VARIATION• Find an equation of variation where y
varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20 and w=2.
VARIATION• Find an equation of variation where y
varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20 and w=2.
2wkxzy
VARIATION• Find an equation of variation where y
varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20 and w=2.
2wkxzy
22203105 k
VARIATION• Find an equation of variation where y
varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20 and w=2.
2wkxzy
22203105 k
k7
VARIATION• Find an equation of variation where y
varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20 and w=2.
2wkxzy
22203105 k
k7
2
7wxzy