The lesson is about introduction to direct variation. identify if the given table of values, graphs shows direct variation.

2. Exploration
If a kilo of rice costs P30, you have to pay
P60 for two kilos and P90 for three kilos and so on.
Number of kilos
of rice (x) 1 2 3 4 5 6 7
Total Cost (y) P30 P60 P90
y/x
1. When x increases, what happens to y?
2. What do you observe about the ratio of y/x?

3. Number of kilos
of rice (x) 1 2 3 4 5 6 7
Total Cost (y) P30 P60 P90 P120 P150 P180 P210
y/x 30 30 30 30 30 30 30
3. Plot the points (x, y) in
the table on the x-y plane.
4. What do you observe
about the points you have
plotted?

4. DIRECT VARIATION
Two quantities are directly proportional if an
increase in one quantity corresponds to a constant
increase in the other quantity, or if a decrease in one
quantity corresponds to a constant decrease in the
other quantity.
X Y
X Y

5. DIRECT VARIATION
• The graph of a direct
variation equation y =
kx is a line with a
slope k, the
constant of variation
and y- intercept,
(0,0)

6. EXAMPLES OF DIRECT VARIATION
The cost of an airplane ticket is proportional
to the number N of miles of the trip.
The amount of salary received is related to
the number of hours worked.
The length of a persons hair is related to the
number of days.

7. TRANSFORM THE FOLLOWING INTO
MATHEMATICAL EQUATION
1. y varies directly as x.
2. Q varies directly as the square of t.
3. V varies directly as the cube of a.
4. M varies directly as the square root of b
5. The electric current (I) varies directly as the
voltage (v)

8. IDENTIFY THE VARIATION CONSTANT
AND THE EQUATION OF VARIATION
x 1 2 3 4
y 5 10 15 20
x 1 2 3 4
y 5 20 60 80