Table à Equation
Do Now
Using the formula for arithmetic sequencing, write an equation for: 3, 5, 7, 9, 11, …
an = a1 + (n – 1)(d)
In the formula for the equation of a line, y = mx + b, what does the m stand for?
Sequence to Table
Remember, a sequence can be represented in a table. Place the sequence 3, 5, 7, 9, … into the following tables.
What is the common difference between each outcome?
Slope
The difference between the outcomes represents the change per one unit. If the difference between the outcomes is consistent, the values represent a linear function! The common difference (rate of change) is also known as slope!
Exercise: What is the slope represented in each example of the worksheet?
y-intercept
The y-intercept is the place where a linear function crosses over the y-axis. What value of x does the y-axis lie on?
Where is the y-intercept in a table of values for a linear function?
Exercise: Find the y-intercept in each example of the worksheet.
Linear Equations
You now have enough information to represent the slope and y-intercept in an equation. The slope-intercept form of a linear function is:
y = mx + b
Exercise: Write an equation to represent each example in the worksheet.
Babysitting
You have been hired by your neighbors to babysit their children on Friday night. You are paid $8 per hour. Complete the table relating your pay to the number of hours you worked.
Write an equation to represent this situation.
How could you use the information to determine the pay for a week in which you worked 20 hours?
Movies
The table below shows the relationship between the cost of renting a movie to the number of days on rent.
Write an equation to represent this situation.
Each table of values represents a linear function.
term / 1 / 2 / 3 / 4outcome / 15 / 20 / 25 / 30
slope = _____
y-intercept = _____
Equation: ______/ term / 4 / 5 / 6 / 7 / 8
outcome / 16 / 14 / 12 / 10 / 8
slope = _____
y-intercept = _____
Equation: ______
term / outcomes
0 / -5
1 / -3
2 / -1
3 / 1
4 / 3
slope = _____
y-intercept = _____
Equation: ______/ term / outcomes
2 / 12
4 / 20
6 / 28
8 / 36
10 / 44
slope = _____
y-intercept = _____
Equation: ______/ term / outcomes
3 / 1
5 / -5
1 / 7
2 / 4
4 / -2
slope = _____
y-intercept = _____
Equation: ______
Name: ______Date: ______
Algebra I CC Exit Ticket
Write an equation for the following table of values:
term / 0 / 1 / 2 / 3 / 4 / 5outcome / 1 / 4 / 7 / 10 / 13 / 16
Equation: ______
Name: ______Date: ______
Algebra I CC Exit Ticket
Write an equation for the following table of values:
term / 0 / 1 / 2 / 3 / 4 / 5outcome / 1 / 4 / 7 / 10 / 13 / 16
Equation: ______
Name: ______Date: ______
Algebra I CC HW
Write an equation for each table of values:
1. /Equation: ______ / 2. /
Equation: ______
3. /
Equation: ______ / 4. /
Equation: ______
Review:
5. If you add 125 to ½ of a number, the result is 450. What is the original number?