2.5.3: Graphing a linear equation using slope and y-intercept.
1)
For y = 3x + 1, where does the line cross the y axis?
0
1
3
2)
For y = 3x + 1, plotting a point when x is 1 yields what y?
3
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3)
For y = 3x + 1, the y-intercept is 1, so a point can be drawn at x = 0 and y = 1, namely up 1 on the y axis. A second point can be drawn by going to the right 1 and going up ___.
1
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4)
For y = -2x + 3, what is the slope?
-2
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5)
What does the equation y = 3 look like when graphed?
A vertical line
A horizontal line
Cannot be graphed
Feedback?

Example: Gym memberships
A common use of linear equations is to graph various options to help choose one. An example is gym membership options. A graph helps a person visualize the options and choose the best given the expected membership duration.
PARTICIPATION ACTIVITY
2.5.4: Example: Gym memberships.
Start
2x speed
Month
Total cost ($)
50
100
150
200
250
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25
1
y = 25x
1
15
y = 15x + 50
1
10
y = 10x + 100
Monthly is cheapest
Platinum is cheapest
Monthly
Standard
Platinum
keyboard_arrow_downCaptions
Feedback?
PARTICIPATION ACTIVITY
2.5.5: Gym memberships.
Consider the example above.
1)
Which line has the most steep slope?
Monthly
Standard
Platinum
2)
Which option is cheapest for 4 months?
Monthly
Standard
Platinum
3)
Which option is cheapest for 6 months?
Monthly
Standard
Platinum
4)
Which option is cheapest for 12 months?
Monthly
Standard
Platinum
Feedback?
Pricing
Companies often contract with pricing experts to help set prices. For the gym example above, the experts created an option (Monthly) with no membership fee to get more people started. The expert also created a low monthly priced option (Platinum) to appeal to people with long-term plans, with a high membership fee to make sure people renew each year (since letting membership lapse and later paying the fee a second time is painful). Above, the pricing expert included a third option, named “Standard” to entice people by suggesting “This option is what most people choose.” People have a strong tendency to copy other humans. (This tendency served a person well in the wild: If everyone sitting in a circle suddenly ran away, the person should probably run too). Note that the Standard plan ends up being costlier than the Platinum plan; the pricing expert hopes members will choose Standard and end up paying that extra $5 per month for a long time.
CHALLENGE ACTIVITY
2.5.1: Graphing via slope/intercept.
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Start
What are the slope and y-intercept in the equation y = 3x + 8?
Slope: y-intercept:
1
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5
6
Check
Next
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