Direct Variation, Constant of Proportionality, and Slope

constant rate of change

Another phrase for slope is

k = 8

Determine the constant of variation: y = 8x

k = 9

Determine the constant of variation: y = 9x

y = -1/4x; x = -80

If x = -16 when y = 4, write the direct variation equation and find x when y = 20.

y = -1/3x; y = -2

If x = -18 when y = 6, write the direct variation equation and find y when x = 6.

y = 2x; y = 40

If x = -7 when y = -14, write the direct variation equation and find y when x = 20.

y = 1/5x; y = 4

If x = 2.5 when y = 0.5, write the direct variation equation and find y when x = 20.

y = 3x; y = -72

If x = 4 when y = 12, write the direct variation equation and find y when x = -24.

y = 0.5x; y = 2.5

If x = 8 when y = 4, write the direct variation equation and find y when x = 5.

y = -4x; x = -5

If y = -16 when x = 4, write the direct variation equation and find x when y = 20.

y = -3x; y = -18

If y = -18 when x = 6, write the direct variation equation and find y when x = 6.

y = 0.5x; y = 10

If y = -7 when x = -14, write the direct variation equation and find y when x = 20.

y = 5x; y = 100

If y = 2.5 when x = 0.5, write the direct variation equation and find y when x = 20.

y = 4.5x; x = 10

If y = 27 when x = 6, write the direct variation equation and find x when y = 45.

y = 6x; x = 7

If y = 36 when x = 6, write the direct variation equation and find x when y = 42.

y = 1/3x; y = -8

If y = 4 when x = 12, write the direct variation equation and find y when x = -24.

y = 2x; y = 10

If y = 8 when x = 4, write the direct variation equation and find y when x = 5.

y = 3/2

If y varies directly with x, write an equation for the direct variation. Then find each value. Find y when x = 1, if y = 3 when x = 2.

26

In a direct variation, y=39 when x=3. Find the value of y when x=2.

Yes

Is this a direct variation equation?

Yes

Is this a direct variation function

No

Is this a direct variation function?

Yes

Is this a direct variation function?

no

Is this a direct variation function?

No

Is this a direct variation function? y - 4 = 9x

yes

Is this a direct variation function? y = 2x

No

Is this a direct variation function? y = 8x + 3

YES K=3

Is this a direct variation? YES or NO If yes what is the direct variation?

NO

Is this proportional? YES or NO If yes what is the direct variation?

k = $33.75

Jerry rents snowmobiles to tourists. He charges $135 for 4 hours and $202.50 for 6 hours. If the cost varies directly with amount of hours find k, the hourly rate Jerry charges to rent a snowmobile?

6

Ohm's Law states that the voltage, V, of an electrical circuit is directly proportional to I, the current. If the current was 1.3 amps when the voltage was 2.6 volts, what would the current be when if the voltage was increased to 12 volts?

27

On a treasure map, the actual distance is directly related to the scaled distance. If 15 miles is represented by 3 centimeters, then how many centimeters on the treasure map are equivalent to 135 miles?

origin

Proportional and direct variation equations pass through the ________.

Proportional

Proportional or non-proportional? y = 2x

Non-proportional

Proportional or non-proportional? y = 3x + 8

777

The money made tutoring directly varies with the time spent tutoring. If a tutoring job pays $222 for 10 hours of work, how much would they make for 35 hours of work?

y = 1.05x

The number of laps a swimmer swims, y, varies directly with the number of minutes spent swimming, x. In 50 minutes, the swimmer swims 52.5 laps. Write a direct variation equation

20

The number of words Maria typed varied directly with the amount of time she spent typing. If she typed 275 words in 5 minutes, how long would it take her to type 1,100 words?

10

What is the constant of proportionality? y = 10x

5

What is the constant of proportionality? y = 5x

1

What is the constant of proportionality? y = x

k = 1.5

What is the constant of proportionality? (type k = ___)

y = 0.20x

What is the equation for this direct variation?

8

What is the slope? y = 8x

½

What is the slope? y = ½x

(0, 0)

What ordered pair does a direct variation equation always go through when graphed?

y = 1/6x; x = 252

y = 1/6x; x = 252 If x = 36 when y = 6, write the direct variation equation and find x when y = 42.

60

y varies directly with x, and y is 15 when x is 9. What is y when x is 36?

y = ½x

y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?

k = 10

y varies directly with x, and y is 40 when x is 4. What is the constant of variation?

16

y varies directly with x, and y is 5 when x is 10. What is x when y is 8?

y = ¼x

y varies directly with x, and y is 7 when x is 28. Which equation represents this situation?

y = 4x

y varies directly with x, and y is 8 when x is 2. Which equation represents this situation?

k = 5

y varies directly with x, and y is 80 when x is 16. What is the constant of variation?