1. Write and graph a direct variation equation.

2. 5.2 Getting ready
The time it takes to hear thunder varies directly with the distance from the lightning.
A function represented by the equation: y = kx where k≠ 0
Direct Variation:
a. The coefficient of x.
b. 𝑘= 𝑦 𝑥
Constant of variation:

3. Determine whether each equation represents a direct variation
Determine whether each equation represents a direct variation? If so, find the constant of variation.
B). 3y + 4x = 8
A). 7y = 2x
A). 7y = 2x
B). 3y + 4x = 8
-4x x
3y = x
3y = x
y = 2x 7
y = 8 – 4x
Is the equation in the form of y = kx?
yes
Is the equation in the form of y = kx?
The constant of
variation is: 2 7
No, so it’s not a direct variation.
Or k = 2 7

4. y = kx 35 = k(5) 7 = k y = 7x y = 7x y = 7(9) y = 63
Suppose y varies directly with x, and y = 35 when x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9?
y = kx
Direction variation equation form:
Solve for k:
35 = k(5)
Use y = 35 and x = 5
7 = k
y = 7x
Write your new equation:
y = 7x
What is the value of y when x = 9?
y = 7(9)
(substitute and solve)
y = 63

5. y = kx y = kx 50 = k(130) .38 = k y = .38x x y Solve for k: Substitute
Weight on Mars y varies directly with weight on Earth x. The weights of the science instruments onboard the Phoenix Mars Lander weigh 50 lbs on Mars and 130 lbs on Earth.
What is an equation that relates weight, in pounds, on Earth x and weight on Mars y?
y = kx
y = kx
Solve for k:
50 = k(130)
Substitute
x =
y =
.38 = k
130 50
y = .38x
Make a table and graph the equation. x y 50
100
150 19 38 57

6. 1. Equation: y= kx 2. Line passes through (0,0)
Graphs of direct variations:
1. Equation: y= kx
2. Line passes through (0,0)
3. The slope of the line = k.
k > 0
k < 0

7. Does y vary directly with x
Does y vary directly with x? If it does, write an equation for the direct variation.
How?
Find k
𝑦 𝑥
𝑦 𝑥 x y 4 6 8 12 10 15 x y -2
3.2 1
2.4 4
1.6
3.2 −2 = -1.6
6 4 = 1.5
2.4 1 = 2.4
12 8 = 1.5
15 10 = 1.5
1.6 4 = .4
Yes. It is a direct variation equation because the ratio 𝑦 𝑥 is the same.
No. It isn’t a direct variation equation because the ratio 𝑦 𝑥 isn ′ t the same.
y = 1.5x

8. Assignment: pg even.