Solve for a.
Warm-Up Exercises
1. 2a10 =
2. 165a = –
3. Write an equation of the line that passes through the points and . ( )0, 0 ( )4, 8
ANSWER 5
ANSWER5
16–
ANSWER 2xy =
4. A flower is 4.5 centimeters wide and has a leaf 7.2 centimeters long. What is the ratio of flower width to leaf length?
ANSWER 5 to 8
Example 1 Graph a Direct Variation Equation
Graph .4
7y x=
Find a second point by substituting a convenient value for x.
4
7y x= Write equation.
4
7y 4= ( ) Substitute 4 for x.
SOLUTION
Plot a point at the origin.
Example 1 Graph a Direct Variation Equation
7y = Simplify.
A second point is .4, 7( )
Plot the second point. Then draw a line through the two points as shown.
Example 2 Write a Direct Variation Equation
Recipes To make mango salsa, replace the tomatoes in the recipe above with mangoes, using 3 mangoes for 2 recipes. Write an equation relating the number of servings y to the number of mangoes x given so that y varies directly with x. How many servings of salsa can you make if you have 5 mangoes?
Example 2 Write a Direct Variation Equation
In 2 recipes there are servings, so 3 mangoes make 8 servings. This means when . Write an equation using these values of y and x to solve for k.
SOLUTION
( )42 8=8y = 3x =
kxy = Write a direct variation equation.
8 = Substitute 8 for y and 3 for x.( )3k
= Simplify.k3
8
An equation is . To find how many servings of
salsa you can make using 5 mangoes, substitute 5 for x.
= x3
8y
Example 2 Write a Direct Variation Equation
= x3
8y =
3
8 ( )53
40= =
3
113
ANSWER
Five mangoes will make about 13 servings.
Checkpoint
The variables x and y vary directly. Write an equation that relates x and y.
5. x = 3, y = 9– ANSWER y = 3x–
6. x = 10, y = 2 ANSWER = x5
1y
Write a Direct Variation Equation
Example 3 Identify Direct Variation
Tell whether the data, the numbers of words y in the first x lines of the Declaration of Independence, show direct variation. If so, write an equation relating x and y.
SOLUTION
Find the ratio of y to x for each data pair.
30.6=5
15330.5=
10
30530.1=
20
60230.27
15
454≈ 30.28
25
757≈
Words, y 305
15
454
20
602
25
757
Lines, x 5 10
153
Example 3 Identify Direct Variation
The ratio of y to x in each pair is nearly the same, so the data show direct variation. Substituting 30.3 for k in y kx gives the direct variation equation y 30.3x.= =
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