Jovie earns money tutoring at a rate of 125 pesos per hour. Her earnings increase directly with the number of hours tutored. The question asks to determine the equation that relates her earnings (E) to the number of hours tutored (t). The document explains that because E and t are directly proportional, their relationship can be written as an equation with a constant of variation. It provides the example relationship E = 125t, where 125 is the constant of variation. Therefore, the equation that determines Jovie's earnings for tutoring t hours is E = 125t.

2. Let’s Learn
Jovie is working as a tutor and earns 125 pesos
per day. In 2 hours she earns 250 pesos. In 3
hours she earns 375 pesos, and so on. What
equation can be used to determine the amount
of money Jovie makes in tutoring?

3. The table below shows the money Jovie makes
corresponding to the number of hours tutoring.
Number of Hours (t) Earnings in Pesos (E)
1 125
2 250
3 375
4 500
In the above situation, the independent variable is
time (t) and the dependent variable is the earnings (E).

4. Obseve that the ratio of earnings to time is
125
1
in each case.
If two variables result in pairs of numbers in which the ratio is
constant, we say that the two variables are in direct variation. In the
above problem, the earnings (E) varies directly with the time (t) with
a common ratio of 125. Then, we may have
𝐸
𝑡
= 125 or E = 125t
Therefore, E = 125t is the equation that determines the
earnings of Jovie for tutoring in t hours. The common ratio in the
variation is known as the constant of variation or constant ratio.

5. Two variables x and y are said to be in direct variation
if it can be expressed as a function y = kx where k is a
constant ratio which is non-zero. We also say that y varies
directly as x. The constant ratio k is the constant of
variation.
Study the following:
Statement Equation
y varies directly as z y = kz
g varies directly as the square of l g = kl2
m varies directly as the square
root of p
m = k 𝑝

6. Example 1. Suppose y = 12 when x = 3. Find the
constant of variation and an equation of variation if y
varies directly as x.
Steps Solution
1. Identify the given. y = 12 when x = 3
y varies directly as x.
2. Determine what is asked for. Find the constant of variation
and the equation of variation.
3. Identify the formula to be
used.
y = kx (1)

7. Steps Solution
4. Substitute the given in the
formula to solve for the constant
of variation
Solve for k when y = 12 and x =
3.
y = kx
12 = k(3)
4 = k
5. Find the equation of variation. Substitute the value of k in (1).
y = kx
y = 4x
6. State the answer. The constant of variation is 4
the equation of variation is y =
4x.

8. Example 2. Suppose y = 5 when x = 16. Find the constant of
variation and an equation of variation where y varies directly
x.
Solution:
y = kx
5 = k(16)
5
16
=
k
16
5
16
= k (constant of variation)
y = kx ; y =
5
16
x
Therefore the constant of
variation is
5
16
and the
equation of variation is y =
5
16
kx.

9. Example 3. If y varies directly as x, when x = 3. Find the
constant of variation and an equation of variation if y = 15.
Solution:
y = kx
15 = k(3)
5 = k (constant of variation)
y = kx
y = 3x(equation of variation)
Therefore, the constant of
variation is 5 and the
of variation is y = 3x.

10. Example 4. Suppose y = 100 when x = 2. What is the
constant of variation when y varies directly as the square
x?
Solution:
y = kx2
100 = k(2)2
100 = k (4)
25 = k (constant of
variation)
Therefore the constant of
variation is 25.