Direct and Inverse Variation

The distance traveled varies directly with the time spent in motion when speed is held constant. If d represents the distance traveled and t represents time, which equation would represent this variation? If you travel 150 miles in 4 hours, what is the constant of variation? If you continue traveling at a constant speed, how long will it take to travel 200 miles? Round to the nearest tenth of an hour.

D=KT 37.5 5.3

Which graph represents a direct variation between the quantities x and y?

Graph C

A quantity, t, varies inversely with a quantity, r. If t = 6, then r = 5. What is the constant of variation? k=? What is the equation that represents this variation? rt =? What is the value of t when r = 15(?)

k=30 rt=30 (2)

The value of z varies inversely with the value of w. The constant of variation is 2/3 . Which are possible values for z and w? Check all that apply.

A C D

Joe plotted the points (2, 0.5), (1, 1), and (0.5, 2), and claimed that these points represent an inverse variation relationship. Which statement supports his claim?

A: xy = 1 for all points

Which statements are true about the table of values? Check all that apply. A: xy = 3 B: When x = 3, y = 1. C: x varies directly with y. D: k =1/3 E: The graph of this table would not be linear.

A: xy=3 B: When x = 3, y = 1 E: The graph of this table would not be linear

Which equations represent inverse variation? Check all that apply. A: y=2x B: pv = 13 C: z=2/x D: 4=y/x E: h=9g/5

B: pv=13 C: z=2/x

When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12. 1. How many inches would a 3.5-foot object measure? 2. How many inches would a 3.5-foot object measure? 3. How many feet would a 27-inch object measure?

1. m=12f 2. 42 3. 2.25