Content Objective:
Sect. 8.4
• WWBAT find the constant of variation.
Language Objective:
• WWBAT write a problem that involves direct variation. You will need graph
paper for the
homework.
Skill Assignment 8.4 pg 407#5­21
Due_____________
1
Page 405
Direct Variation (Proportional)
Voc
a
Boo b k
A linear function that
goes through the point
(0,0). The equation is
in the form y =kx, k≠0.
(k is slope)
Constant of Variation
The name given to the
slope or k value when a
linear equation is
proportional or varies
directly.
Voc
a
Boo b k
If you see k = 5, then you know that the slope is 5 and the y­intercept is 0.
This is a fancy name for the slope of a proportional relationship.
2
White Board Time
3
Page 405
Use y = kx and the values given to find k.
Remember y is said to vary with x.
White Board Time
4
Page 406
White Board Time
Can you think of some situations that vary directly? Remember what needs to happen from a relation to vary directly:
1. Weight on Earth varies directly with the weight on the moon.
2. Distance traveled varies directly with time (at a constant rate)
3. The number of words typed varies directly with time (at a constant rate)
4. The tax you are charged varies directly with the amount you spend on taxable items.
5. The amount you earn varies directly with the time you work (if you are paid at an hourly rate.
Talk to your partner!
1.) Take out a piece of paper and make a problem in which the variables vary directly (or are proportional). 2.) Exchange it with your partner and solve for the constant of variation.
3.) Write the equation that describes the situation you were given.
4.) Exchange back and see if you agree with the solution you were given.
5