Direct and Inverse Variation
Algebra I
Direct Variation
• When the line passes through the origin.
• When y increases, x increases.• Equation: y = kx, where k 0.• Constant of variation – k• Say “ y varies directly with x”
Identifying the constant of variation
y = 6x
6 is the constant of variation (k)
These can be graphed on the calculator using ‘y=‘ button, to see what the graph should look like.
Examples:
y = 28, x = 7 find x when y = 52
Examples:
y = 28, x = 7 find x when y = 52
y = kx y = kx
Examples:
y = 28, x = 7 find x when y = 52
y = kx y = kx28 = k(7) 52 = 4x 7 7 4 44 = k 13 = x y = 4x
Example:
y = 27, x = 6 find x when y = 45
Example:
y = 27, x = 6 find x when y = 45
27 = k(6) 45 = 9/2x 6 6 (2/9)45 = x9/2 = k 10 = x
Y = 9/2x
Example:
y = -7, x = -14 find y when x = 20
Example:
y = -7, x = -14 find y when x = 20
-7 = k(-14) y = (½)20-14 -14 y = 10½ = k
y = ½x
Inverse (Indirect) Variation
• Line going away from the origin.• When one value (x or y) increases, the
other value (x or y) decreases.• Equation xy = k • Say “y varies inversely as x” or “y is
inversely proportional to x”.
Different forms of the equation
xy = k
Y = k/x or x = k/y
Example:
If y = 12 when x = 5, find y when x = 3
xy = k 3y = 60(5)(12) = k 3 3 60 = k y = 20
xy = 60
Example:
If y = 7, when x = -2; find y when x = 7
If y = 8.5, when x = -1; find x when y = -1
If y = 8, when x = 1.55; find x when y = -0.62
Example:
If y = 7, when x = -2; find y when x = 7 xy = -14 y = -2
If y = 8.5, when x = -1; find x when y = -1 xy = -8.5 x = 8.5
If y = 8, when x = 1.55; find x when y = -0.62 xy = 12.4 x = -20
Top Related