VARIATIONS(Direct Variation for Grade 9 students

Discussion for second quarter 2 lesson

1. VARIATIONS Direct and inverse

2. Objectives: Illustrate situations that involve direct variation Translate into variation statement a relationship involving direct variation between two quantities given by a table of values, a mathematical equation, a graph and vice versa; Solve problems involving direct variation

3. Direct variation There is a direct variation whenever a situation produces pairs of numbers in which their ratio is constant. This can be expressed into mathematical statement or equation as y = kx , where k = y/x is the constant of variation or constant of proportionality. These statements can “y varies directly as x” “y is directly proportional to x” and “y is proportional to x” These statements mean that for two quantities, x and y, an increase in x causes an increase in y as well. Similarly, a decrease in x causes a decrease in y.

4. Example: Using his bicycle, Kyle travels a distance of 10 kilometers per hour on a steep road. Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50 Show that distance (d) varies directly as time (t). b) Draw the graph of d against t. c) Write an equation showing the relationship between d and t. d) How far Kyle travelled after 8 hours and 10 ½ hours?

5. Example: Using his bicycle, Kyle travels a distance of 10 kilometers per hour on a steep road. Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50 Show that distance (d) varies directly as time (t). Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50             is constant, d varies directly as t.

6. Example: Using his bicycle, Kyle travels a distance of 10 kilometers per hour on a steep road. Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50 b) Draw the graph of d against t.

7. Example: Using his bicycle, Kyle travels a distance of 10 kilometers per hour on a steep road. Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50 c) Write an equation showing the relationship between d and t. Because , the equation relating d and t is  

8. Example: Using his bicycle, Kyle travels a distance of 10 kilometers per hour on a steep road. Time ( hr ) 1 2 3 4 5 Distance (km) 10 20 30 40 50 d) How far Kyle travelled after 8 hours and 10 ½ hours? t = 8 d = 10t = 10(8) = 80 t = 10 ½ d = 10t = 10(10 ½) = 105

9. Example 2: write an equation for the following statements The fare F of a passenger varies directly as the distance d of his destination. The weight W of an object is directly proportional to its mass m . The area A of a triangle is proportional to its height h .

10. Example 3: if Y VARIES DIRECTLY AS X, AND Y = 24 WHEN X = 6, FIND THE VARIATION CONSTANT AND THE EQUATION OF VARIATION.