What is the relationship between two variable quantities that have a constant ratio called?
Direct Variation
100
Determine whether each linear function is a direct variation. If so, what is the constant of variation?
Gallons (x): 6, 8, 10, 12
Miles, (y): 180, 240, 300, 360
Yes
30 miles per gallon
100
If y varies directly with x, write an equation for the direct variation. The find each value. Remember y = kx.
If y = -4 when x = 10, find y when x = 5
-2
100
The number of home theaters a company sells varies directly as the money spent on advertising. How many home theaters does the company sell for each $500 spend on advertising? (See Graph from teacher)
8
200
What is the constant ratio in a direct variation called?
Constant of Variation
200
Determine whether each linear function is a direct variation. If so, what is the constant of variation?
Time (min), (x): 10, 12, 12, 13
Temperature, (y): 82, 83, 84, 85
No
200
If y varies directly with x, write an equation for the direct variation. The find each value. Remember y = kx.
If y = 12 when x = -15, find y when x = 2
-1.6
200
The number of place settings of dishes varies directly with the number of boxes. How many place settings are in each box? (See Graph from teacher)
4
300
What is the constant ratio or unit rate of two variable quantities called?
Constant of Proportionality
300
Determine whether each linear function is a direct variation. If so, what is the constant of variation?
Number of Payments, (x): 6, 11, 16, 21
Amount Paid, (y): $1500, $2750, $4000, $5250
Yes
$250 per payment
300
If y varies directly with x, write an equation for the direct variation. The find each value. Remember y = kx.
Find x when y = 18, if y = 9 when x = 8
16
300
Kentish is arranging figurines on shelves. The number of figurines varies directly with the number of shelves. What is the constant of proportionality?