Algebra 1 Common Core Student Edition, Grade 8-9

For the data in each table, tell whether y varies directly with x. If it does, write an See Problem 4.

equation for the direct variation. Check your answer by plotting the points from

the table and sketching the line.

27.

an

-6^9

1 -1.5

8 -12

28.

an

35.4

712.6

12 21.6

29.

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8 11

Q Apply Suppose y varies directly with x. Write a direct variation equation that relates
x andy. Then graph the equation.

30. y = 2 w h e n x = 3. 31. y =- 5 w h e n x = 4. 32. y = g w h e n x = 33. y = 7.2 w h en x = 1.2.


31. Think About a Plan The a m o u n t of blood in a p e rso n ’s body varies directly w ith
    body weight. A p erso n w ho w eighs 160 lb h as ab o u t 4.6 q t of blood. A bout how
    m any quarts of blood are in th e b ody of a 175-lb person?
    
    
    • How can you find th e co n stan t of variation?
    
    
    • Can you write an equ atio n th at relates quarts of blood to weight?
    
    
    • How can you use the eq u a tio n to d eterm in e th e solution?
    
    
    
    

^22) 35. Electricity Ohm's Law V= IX R relates th e voltage, current, a n d resistance of a

circuit, h i s th e voltage m easu red in volts. I is th e cu rren t m easu red in am peres. R is

th e resistance m easu red in ohms.

a. Find th e voltage of a circuit w ith a cu rren t of 24 am p eres an d a resistance of 2 ohms.

b. Find the resistance of a circuit w ith a current of 24 am peres an d a voltage of 18 volts.

Reasoning Tell whether the two quantities vary directly. Explain

your reasoning.

36. th e n u m b e r of ounces of cereal a n d th e n u m b e r of Calories th e cereal contains


37. th e tim e it takes to travel a certain d istance an d th e rate at w hich you travel


38. th e p erim e te r of a square an d th e side length of th e square


39. th e a m o u n t of m on ey you have left an d th e n u m b e r of item s you p urchase


40. a. G raph th e following direct variation eq u a tio n s in th e sam e coordinate plane:
    y = x, y = 2x, y = 3x, an d y = 4x.
    b. Look fo r a Pattern D escribe h o w th e graphs change as th e co n stan t of
    variation increases.
    c. Predict how th e graph of y = \x would appear.


41. Error Analysis Use th e table at th e right. A stu d e n t says th a t y varies directly w ith
    x because as x increases by 1, y also increases by 1. Explain th e stu d e n t’s error.


42. Writing Suppose y varies directly with x. Explain how th e value of y changes in
    each situation.
    a. The value of x is doubled. b. The value of x is halved.

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PowerAlgebra.com [ Lesson 5-2 Direct Variat io n