5.2 direct variation

Write and graph a direct variation equation.

5.2 Getting ready

The time it takes to hear thunder varies directly with the distance from the lightning.

Direct Variation: A function represented by the equation: y = kx where k≠ 0

Constant of variation:a. The coefficient of x. b.

Determine whether each equation represents a direct variation? If so, find the constant of variation.

A). 7y = 2x7 7

A). 7y = 2x

y = 2x 7

Is the equation in the form of y = kx?

The constant of variation is:

2 7

Or k = 2 7

B). 3y + 4x = 8B). 3y + 4x = 8-4x - 4x

3y = 8 - 4x3y = 8 - 4x3 3 3

y = 8 – 4x 3 3

Is the equation in the form of y = kx?yes

No, so it’s not a direct variation.

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?

Direction variation equation form: y = kx Solve for k: 35 = k(5)

7 = k

Write your new equation: y = 7x

What is the value of y when x = 9?

(substitute and solve) y = 7(9)y = 63

y = 7x

Use y = 35 and x = 5

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?

Make a table and graph the equation.x y

y = kx Solve for k:

Substitute x = y =

13050

y = kx 50 = k(130) .38 = k

y = .38x

0 50100150

0193857

Graphs of direct variations:

1. Equation: y= kx2. Line passes through (0,0)

3. The slope of the line = k.

k > 0 k < 0

x y

4 68 1210 15

x y

-2 3.21 2.44 1.6

Does y vary directly with x? If it does, write an equation for the direct variation.

How? 𝑦𝑥

= 1.5

= 1.5

= 1.5

Yes. It is a direct variation equation because the ratio is the same.

𝑦𝑥

= -1.6

= 2.4

= .4

No. It isn’t a direct variation equation because the ratio

Find k

y = 1.5x

Assignment: pg 304 10-38 even.