Rate of Change and Initial Value

Rate of Change

Multiple Representations

y=mx+b

M is the RATE OF CHANGE

this is the number being multiplied (or divided)

B is the INITIAL VALUE

this is the number being added (or subtracted)

Multiple Choice

Identify the m and b in the following equation:

y = 2x + 5

• m = 5

  b = 2

• m = 2

  b = 5

• m = y

  b = x

How to find M (rate of change)

from TABLES, GRAPHS, and WORD PROBLEMS

Find M from a table

 $\frac{y2\ -\ y1}{x2\ -x1}$  

Multiple Choice

Determine the slope from the table.

• -2

• 2

• -1/2

• 1/2

Multiple Choice

What is the slope?

• 2

• 1/2

• 1

• 1.5

Multiple Choice

What is the slope?

• -1/3
• -3
• -4
• 5

Find M from a graph

 $\frac{y2-y1}{x2-x1}$ 

 $\frac{Rise}{Run}$  

Open Ended

What do you notice about these 2 lines?

Negative vs Positive slope

Multiple Choice

How do you calculate slope using a graph?

• rise over run

• run over rise

• look at the y intercept

• look at the x intercept

Multiple Choice

Describe the slope

• Positive

• Negative

Multiple Choice

Describe the slope

• Positive

• Negative

Multiple Choice

Find the slope

• -5/6

• 4/3

• 3/4

• -4/3

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Find B from a table

Initial value is y, when x = 0

Multiple Choice

What is the initial value?

• 1/2

• 2

• 7

• 3

Multiple Choice

What is the y-intercept (initial value)?

• (0,2)

• (6,0)

• (2,0)

• (0,6)

What if there is no 0 in the table?

First find the Rate of Change (m)

Do m times x

Find what you need to add to the product to equal y

Multiple Choice

First find the rate of change. (m)

• 15

• 3

• 1/3

• -6

Multiple Choice

Now use m = 3, to solve for the initial value (b)

Remember m(x)+b = y

• 7

• 1

• 3

Find B from a graph

Find where the line goes across the Y-Axis

The value of y, when x is 0, is the inital value (b)

Multiple Choice

What is the initial value (b)?

• 1

• -1

• -3

• 3

Multiple Choice

What is the y-intercept (b) of the graph?

• (0,-1)

• (0,1)

• (-1,0)

• (1,0)

Multiple Choice

What is the initial value (b) of the line?

• 5

• 7

• 1.25

• -5

Writing an equation

y = mx +b

Find total (y)

Find # being multiplied/divided (m)

Find # being added/subtracted (b)

Multiple Choice

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which number represents the rate of change (m)?

• 80

• 15

Multiple Choice

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which number represents the initial value (b)?

• 80

• 15

Multiple Choice

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

• y=15x

• y=15x+80

• y=x+15

• y=80x+15