SLOPE Monday 11/14 Effects of SLOPE with changes to m and b.
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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
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