1.9 - Direct Variation

1.9 - Direct Variation

​Direct Variation

• ​The table displays the distance a car travels, y, after x amount of hours.

• ​1.) What is the constant ratio? Is it proportional?

• ​2.) What is the rate of change? Or the slope?

• ​3.) What do you notice about our two answers?

​Direct Variation

• ​When two quantities have a constant ratio (unit rate) - their relationship is called a direct variation

• ​When two quantities vary directly, the graph will always go through the origin

• ​When writing equations, the direct variation, rate of change, slope, unit rate = k

• ​y = kx

Multiple Choice

The height of the water as a pool is being filled is shown in the graph. Determine the rate.

• 0.4 inch every minute

• 0.4 minute every inch

• 2.5 inches every minute

• 2.5 minutes every inch

Multiple Choice

Two minutes after a diver enters the water, he has descended 52 feet. After 5 minutes, he has descended 130 feet. At what rate is the scuba diver descending?

• 12 ft/min

• 0.04 ft/min

• 26 min/ft

• 26 ft/min

​Writing Equations

• ​The form (y = kx)

• ​Find the unit rate, slope, rate of change and replace K with the value

• ​Example: A group bought tickets for an upcoming volleyball game. They bought 2 tickets for $15, 4 tickets for $30, and 7 tickets for $52.50. Is there a direct variation? If so, write an equation.

Fill in the Blanks

Two weeks ago, Audrey earned $84 for 7 hours of work. This week, she earned $132 for 11 hours of work. Write an equation in the form y = kx that relates Audrey's earnings y to the amount of hours worked x.

Fill in the Blanks

The graph displays the speeds of two cars. Since the graph is proportional, that means that the distance traveled y and the time x varies directly. Write an equation in the form y = kx for Car B.

Open Ended

Pizzas cost $8 each plus a $3 delivery fee. The table displays the cost for 1, 2, 3, and 4 pizzas. Is there a direct variation? Is this relationship linear (would it form a straight line if we were to graph it)?

Multiple Choice

Does the table display a direct variation? If so, use the constant of proportionality to write an equation in y = kx.

• No, the rates are not the same so there is no equation.

• Yes, y = 12x

• Yes, y = 1/12x

• Yes, 12 = kx