Direct Variation - 1st

​Direct Variation

By Carroll Hopkins

A.2D - Write and solve equations involving direct

variation. 

Essential Question

How can I find the solution to problems that are directly proportional?

​y = Y axis variable
x = X axis variable
k = Constant of Variation                          

                               
Our graph will ALWAYS go
through the ORIGIN (0,0)    

​Direct Variations are also called DIRECTLY PROPORTIONAL!

​Constant of Variation

The CONSTANT OF VARIATION is ALSO KNOWN AS:

 

-

 

-
-

 

​Constant of Variation

The CONSTANT OF VARIATION is ALSO KNOWN AS:

 

- SLOPE

 

- RATE OF CHANGE
- m

 

Multiple Choice

$$y=-6x$$

What is the RATE OF CHANGE?

• $$6$$

• $$2$$

• $$-6$$

• $$\frac{1}{6}$$

Finding the Constant of Variation (k) Given Data

STEP 1: Set up data to be x-values and y-values
STEP 2: Desmos table - input the values given & (0,0)
STEP 3: y₁~mx₁+b
STEP 4: Find m (m = k, these are the same!)

​I DO - Finding the Constant of Variation (k)

The value of y varies directly with x. When the value of x is 4, the value of
y is -12. What is the constant of variation?

What is m?

Multiple Choice

The value of y varies directly with x. When the value of x is 2, the value of
y is 8. What is the constant of variation?

• 2

• 4

• 8

• -2

Multiple Choice

The value of y varies directly with x. When the value of x is -4, the value of
y is -8. What is the constant of variation?

• -8

• -2

• 4

• 2

Finding an x value or a y value

STEP 1: Set up data to be x-values and y-values
STEP 2: Desmos table - input the values given
STEP 3: y₁~mx₁+b
STEP 4: Find m (m = k, these are the same!)
STEP 5: Type in the given value:
x =
OR y =
STEP 6: Find where the two lines intersect

I DO - Finding an x value or a y value

The value of y varies directly with x. When the value of x is 4, the value of
y is -12. What is the value of y when x = -6?
STEP 1: x and y are identified
STEP 2:


STEP 3: y₁~mx₁+b
STEP 4: Find m (m = k, these are the same!)
STEP 5: Type in the given value:
x = -6
STEP 6: Find where the two line intersect
What is the y-value where they intersect?

​x	y​
​4	-12​

​You DO

The value of y varies directly with x. When the value of x is 3, the value of
y is 1. What is the value of x when y = 3?

Multiple Choice

The value of y varies directly with x.

When the value of x is 4, the value of y is 2.

What is the value of x when y = 3?

• $$\frac{1}{2}$$

• $$6$$

• $$5$$

• $$2$$

Multiple Choice

The value of y varies directly with x.

When the value of x is 3, the value of y is 1.

What is the value of y when x = 6?

• $$\frac{1}{2}$$

• $$6$$

• $$5$$

• $$2$$

Multiple Choice

The value of y is directly proportional to the value of x.

When x = 512, y = 128.

What is the value of y when x = 64?

• 256

• 32

• 16

• 8

Multiple Choice

The following relationship is DIRECTLY PROPORTIONAL.

At her landscaping job, Daisy makes 60 dollars for every every 3 hours she works. How much will she make after 5 hours of work?

• $15

• $300

• $120

• $100