1. 1.11 Modeling Variation

2. Direct Variation
Distance (d mi) 70
140
210
280 ….
Time (t hrs) 1 2 3 4
We say that the distance varies directly, or is directly proportional to time.

3. Direct variation can be described by an equation of the form y = kx, where k is a non-zero constant called the variation constant or the constant of proportionality.
y = kx y x O
slope = k

4. Inverse Variation side A (cm) 5 10 15 20 …. side B (cm) 60 30
Consider a rectangle with a fixed area of 300 cm2: A B
side A (cm) 5 10 15 20 ….
side B (cm) 60 30
At the end of this slide, show that inverse variations have equations of the form y = k/x.
We say that side A varies indirectly, or is indirectly proportional to side B.

5. Joint Variation h b
Since neither b nor h is fixed, then A varies directly with both b and h.
At the end of this slide, show that joint variations have equations of the form y = kxz.
We say that area A varies jointly as the base b and the height h, or is jointly proportional to b and h.

6. Sample Variation Equations
If z varies jointly with x and y, then z = kxy.
If y varies inversely with the square of x, then
If z varies directly with y and inversely with x, then

7. Write the equation: y varies directly with x and inversely with z2 :
y varies inversely with x3:
y varies directly with x2 and inversely with z :
z varies jointly with x2 and y :
y varies inversely with x and z :