Direct Variation What is it and how do
- Slides: 30
Direct Variation What is it and how do I know when I see it?
Definition Direct Variation – a special type of linear relationship that can represented by a function in the form y = kx, p Constant of Variation – is k, the coefficient of x, in the function y = kx. p
Direct Variation A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings. The equation y = 5 x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice.
Determine Direct Variation from a Table What happens if you solve y = kx for k? y = kx Divide both sides by x (x ≠ 0). So, in a direct variation, the ratio constant of variation. is equal to the
Example: Determine Direct Variation from a Table Tell whether the relationship is a direct variation. Explain. Find for each ordered pair. This is a direct variation because each ordered pair. is the same for
Examples of Direct Variation: What is the constant of variation of the table above? Since y = kx we can say Therefore: 12/6=k or k = 2 14/7=k or k = 2 16/8=k or k =2 Note k stays constant. y = 2 x is the equation!
Examples of Direct Variation: What is the constant of variation of the table above? Since y = kx we can say Therefore: 30/10=k or k = 3 15/5=k or k = 3 9/3=k or k =3 Note k stays constant. y = 3 x is the equation!
What is the constant of variation for the following direct variation? 1. 2. 3. 4. 2 -2 -½ ½ Answer Now
Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!
Which is the equation that describes the following table of values? 1. 2. 3. 4. y = -2 x y = 2 x y= ½x xy = 200 Answer Now
We can find the constant of proportionality from a table of values, equation and a graph. In a table, simplify any one of the ratios. Chaperones 1 2 3 4 5 Students 12 24 36 48 60
Example: Find the constant of proportionality: Apples (lbs) 2 2. 5 3 3. 5 4 Cost ($) 3. 96 4. 95 5. 94 6. 93 7. 92
Using Direct Variation to find unknowns (y = kx) Given that y varies directly with x, and y = 28 when x=7, Find x when y = 52. HOW? ? ? 2 step process 1. Find the constant variation k = y/x or k = 28/7 = 4 k=4 2. Use y = kx. Find the unknown (x). 52= 4 x or 52/4 = x x= 13 Therefore: X =13 when Y=52
We can find the constant of proportionality from a table of values, equation and a graph. In a table, simplify any one of the ratios. Chaperones 1 2 3 4 5 Students 12 24 36 48 60
Find the constant of proportionality: Apples (lbs) 2 2. 5 3 3. 5 4 Cost ($) 3. 96 4. 95 5. 94 6. 93 7. 92 Click
Find the constant of proportionality: X Y 3 4. 5 4 6 5 7. 5 8 12 9 13. 5 Click
Joke Time How would you describe a frog with a broken leg? p Unhoppy p What did the horse say when he got to the bottom of his feed bag? p That’s the last straw! p p What kind of music do chiropractors listen to?
the ORIGIN!!!!!
A Graph is a direct variation if: ê It is a straight line that passes through the origin (0, 0)
Tell if the following graph is a Direct Variation or not. No No Yes No
Tell if the following graph is a Direct Variation or not. No Yes No
Is the relationship shown in the graph proportional? Yes No Salary ($) 41 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 Hours 6 7 8 9 10
Is the relationship shown in the graph proportional? Yes No Cost ($) 42 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 Toppings 7 8 9 10
Is the relationship shown in the graph proportional? Yes No Seconds 43 5 4 3. 5 3 2. 5 2 1. 5 1 0. 5 0 1 2 3 4 5 6 Feet 7 8 9 10
Is the relationship shown in the graph proportional? Yes No Cost ($) 44 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 Text Messages 7 8 9 10
Constant of Proportionality The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y= kx, where k is a
Constant of Proportionality Equation for constant of proportionality is y = kx We can tell that the relationship is directly proportional by looking at the graph. The graph is a straight line that passes through the origin.
Constant of Proportionality Equation for constant of proportionality is y = kx Create a table using the points from the graph: Total price (y) Total pounds (x) Divide total price by total pounds 20 40 60 80 100 2 4 6 8 10
Constant of Proportionality Equation for constant of proportionality is y = kx Create a table using the points from the graph: Total price (y) 20 40 60 80 100 Total pounds (x) 2 4 6 8 10 Divide total price by total pounds 10 10 10
In a graph, choose a point (x, y) to find and simplify the ratio. Students 60 (2, 24) 54 48 42 36 30 24 18 12 6 0 1 2 3 4 5 6 Chaperones 7 8 9 10
