SLOPE Monday 11/14

Effects of SLOPE with changes to

m and b

List two examples of slope in the real world

Real World Equation Please give an real life example of a linear equation. My

example was getting my car fixed. I paid $550 for parts, and $70 per hour for labor. y = 70x + 550 After working 10 hours on my car, the total cost was:

x y = mx + b y

10 70(10) + 550 $1250

Zero Slope No Slope

Change in “b” Graph the following four equations in your

graphing calculator and summarize what happens to your graph as you change b.

1. y1 = x

2. y2 = x + 1

3. y2 = x + 3

4. y2 = x + (1/2)

Change in “b” Graph the following four equations in your

graphing calculator and summarize what happens to your graph as you change b.

1. y1 = x

2. y2 = x - 2

3. y2 = x – (1/2)

4. y2 = x -1

Change in m Graph the following six equations in your

graphing calculator: y1 = x1. y2 = 2x

2. y2 = 5x

3. y2 = -2x

4. y2 = (1/2)x

5. y2 = (-1/4)x

6. y2 = (7/2)x

Change in m How does changing the value affect the

graphs?

Change in m Does changing the m effect the y-intercept?

Change in m If m = 0 how does this affect the graph?

Change in m If m is greater than 0 how does this affect

the graph?

Change in m If m is less than 0 how does this affect the

graph?

Change in m What if there were no slope. How would

this affect the graph?

What is m?slope

rage of changeΔyΔx

y2-y1

x2-x1

riserun

multiplier

Example 1 Given the equation y = 2x + 3,

what would be the result if the slope is multipled by -2 and the y-intercept increased by 5.

Example 2 Given the equation y = x + 5, what happens

to the graph of the line if the slope is increased to 4?

Example 3 A landscape supply

business charges $30 to deliver mulch. The mulch costs $23 per cubic yard. Write the equation.

y = 23x + 30 1. What would happen to the equation if the

delivery charge was changed to $45? 2. What would happen to the equation if the

delivery charge was changed to $15?

y = 23x + 30 1. What would happen to the graph of the

equation if the cost per cubic yard changed to $30.

2. What would happen to the graph of the equation if the cost per cubic yard changed to $10.

Example 4 A cable company

charges $44 for basic service. Each premium channel costs $16 per channel. Write an equation representing your cable bil.

y = 16x + 44 1. What would happen to the equation if the

basic service charge was changed to $50 2. What would happen to the equation if the

basic service charge was changed to $25

y = 16x + 44 1. What would happen to the equation if the

cost per premium channel changed to $10 2. What would happen to the equation if the

cost per premium channel changed to $20