Direct Variation

If y varies directly with x, and the constant of variation is equal to 4, what is x when y=16?

4 (y=4x-->16=4x-->x=4)

If y varies directly with x, and the constant of variation is equal to 3, what is y when x=15?

45 (y=3x-->y=3(15)-->y=45)

If y varies directly with x, and y=12 when x=4, what is the equation that describes this direct variation?

y=3x (k=12/4=3)

What is the general form of direct variation?

y=kx

A line is written in standard form (Ax+By=C). If the line represents direct variation, what does the C value equal?

0

If a scenario shows direct variation, the scenario must be linear (have a constant rate of change), and the initial value must be _________.

0

The slope-intercept form of a line is y=mx+b. In direct variation, what does the b-value equal?

0

Which of the following scenarios shows direct variation? A) Population growth B) The profit from investing $70 to make a business and then making $7 from each widget sold C) The distance that a horse galloping at a constant rate covers D)The distance covered by a falling object

C (There is a constant rate of change and the initial value is 0)

y/x is always a ____________ in direct variation.

Constant

Which of the following equations shows direct variation? A) 3x-5y=7 B) 5x-5y=5 C) 2x-7y=-13 D) 23x-17y=0 E) None of the above

D (When D is transformed into the form y=mx+b, there is no b value)

True or False: Ed has an jug containing 200 ml of water, and Ed pours the water out at a rate of 50 ml per second. The amount of water in the cup in relation to the number of seconds passed is an example of direct variation.

False. (Before the water is poured out, there are 200 ml of water in the jug; therefore, the initial value is not 0)

True or False: An electrician charges an initial service charge of $30 and then an additional $25 for every hour that he works. The cost of the electrician's service in relation to time is an example of direct variation.

False. (The electrician has already charged $20 before starting the job; therefore, the initial value is not 0.)

An ordered pair satisfies a direct variation equation. If the x-value and the y-value are each _____________ by a constant to form a new coordinate, the new coordinate satisfies the original equation.

Multiplied

What is k in the general form of direct variation?

The constant of variation

Direct variation lines always cross through which point?

The origin

Graph y=3x and state whether or not it is an example of direct variation.

This line is an example of direct variation.

Graph y=2x-4 and state whether or not it is an example of direct variation.

This line is not an example of direct variation.

True or False: A car travels at a constant rate of 50 miles per hour. The distance the car travels as time progresses is an example of direct variation.

True. (There is a constant rate of change, and when no time has passed the car has traveled a distance of 0 miles; therefore, the initial value is 0.)