4.5 Notes Alg1.notebook November 26, 2012
Skills we've learned
Skills we need
1. Find the slope of the line that contains (5, 3) and (–1, 4).
2. Find the slope of the line. Then tell what the slope represents.
3. Find the slope of the line described by x + 2y = 8.
45 Direct Variation
Warmup Answers
4.5 Notes Alg1.notebook November 26, 2012
45 Direct Variation
1. Identify, write, and graph direct variation.
Chefs can use direct variation to determine ingredients needed for a certain number of servings.
Direct Variation Introduction: y = kx
A direct variation is a special type of linear relationship that can be written in the form y = kx, where k is a nonzero constant called the constant of variation.
A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a she needs 1 cup of rice for every 5 servings.
The equation y = 5x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice.
Building
Vocabulary
4.5 Notes Alg1.notebook November 26, 2012
I. Identifying Direct Variations from Equations
Tell whether the equation represents a direct variation. If so, identify the constant of variation
1. y = 3x 2. y + 5x = 0 3. x + y = 4
4. –4x + 3y = 0
Solve the equation for y and see if it is in the form y = kx.
Tell whether the equation represents a direct variation. If so, identify the constant of variation
5. 3y = 4x + 1 6. y + x = 0
4.5 Notes Alg1.notebook November 26, 2012
PS. "y over x" is the rate of change, slope!
II. Identifying Direct Variation from Tables
7. Tell whether the relationship is direct variation. If so, identify the constant of variation
Method 1 Write an equation.y = 3xEach yvalue is 3 times the
corresponding xvalue. Method 2 Find for each ordered pair.
8. Tell whether the relationship is direct variation. If so, identify the constant of variation
Method 1 Write an equation.
Method 2 Find for each ordered pair.
y = x – 3 Each yvalue is 3 less than the corresponding xvalue.
4.5 Notes Alg1.notebook November 26, 2012
9. Tell whether the relationship is direct variation. If so, identify the constant of variation
10. Tell whether the relationship is direct variation. If so, identify the constant of variation
III. Writing and Solving Direct Variations
11. The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21.
Method 1 Find the value of k and then write the equation.
y = kx Write the equation for a direct variation.
3 = k(9) Substitute 3 for y and 9 for x. Solve for k. Since k is multiplied by 9, divide both sides by 9
The equation is When x = 21, y =
Method 2 Use a proportion
4.5 Notes Alg1.notebook November 26, 2012
12. The value of y varies directly with x, and y = 4.5 when x = 0.5. Find y when x = 10.
Method 1 Find the value of k and then write the equation.
Method 2 Use a proportion.
IV. Graphing Direct Variations
13. A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph.Step 1 Write a direct variation equation.
Step 2 Choose values of x and generate ordered pairs.
Step 3 Graph the points and connect.
4.5 Notes Alg1.notebook November 26, 2012
14. The perimeter y of a square varies directly with its side length x. Write a direct variation equation for this relationship. Then graph.
Step 1 Write a direct variation equation.
Step 2 Choose values of x and generate ordered pairs.
Step 3 Graph the points and connect.
V. Finding Direct Variation Using a Point
15. Each ordered pair is a solution of a direct variation. Write the equation of direct variation. Then graph your equation and show that the slope of the line is equal to the constant of variation.
A. (2, 30) B. (4, 6)
4.5 Notes Alg1.notebook November 26, 2012
16. Each ordered pair is a solution of a direct variation. Write the equation of direct variation. Then graph your equation and show that the slope of the line is equal to the constant of variation.
A. (3, 15) B. (2, 2)
45 p.263 #2, 3, 5 7, 9, 11, 12, 14, 15, 17, 21, 34, 36, 37, 41