Functions
Linear Functions
Linear or Non-Linear Functions
Writing Linear Equations
Writing Linear Equations #2
100
What is a function?
Each input is assigned exactly one output.
100
What is the equation of this linear function?
It is y = (-1/3)x + 5
100
Does this graph represent a linear function?
Yes, it's a linear function!
100
In a linear equation, which variable represents rate of change?
The variable m.
100
In a linear equation, which variable represents the initial value?
The variable b.
200
Does this table represent a function?
Yes, it's a function!
200
What is the equation of this linear function?
It is y = 4x + 6.
200
No, it's a non-linear function!
200
An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping. What linear equation represents this situation?
The linear equation is y = 6.5x + 3.99.
200
Tara wants to rent a tent for an outdoor celebration. One company charges a $100 set-up fee and $350 per hour to rent their tent. What is the linear equation that represents this situation?
The linear equation is y = 350x + 100.
300
Does this graph represent a function?
Yes, it's a function!
300
What test is used to determine if a graph is a function or not?
The Vertical Line Test
300
Without a graph, how do you determine if a function is linear or non-linear?
Calculate rate of change (or slope).
300
A line has a slope of 1/3 and goes through the point (0,6). What is the linear equation that represents this line?
The linear equation is y = (1/3)x +6
300
A line has a slope of -5 and goes through the point (-2, 3). What is the linear equation that represents this line?
The linear equation is y = - 5x - 7.
400
Does this mapping (arrow) diagram represent a function?
Yes, it's a function!
400
Which linear function has the greater rate of change? What is the rate of change for each panda?
The table has a greater rate of change. Mochi has a rate of change of 4 lbs/week. Kappa has a rate of change of 3 lbs/week.
400
Does this table represent a linear function?
No, it's a non-linear function!
400
What is the slope for a line that runs through the points (3, 11) and (9, 7)?
It is (-2/3)
400
What is the linear equation for a line that runs through the points (3, -1) and (9, -5)?
The linear equation is y = (-2/3)x + 1.
500
(-1, 3), (0, 2), (1, 1), (2, 0), (0, 3)
Does this set of ordered pairs represent a function?
No, it's not a function!
500
Which linear function has a greater initial value? What is the initial value for each panda?
The graph has a greater initial value. Mochi has an initial value of 1 lb. Kappa has an initial value of 2 lbs.
500
Does this table represent a linear function?
Yes, it's a linear function!
500
A store sales packages of comic books with a poster. One package containing 6 comics (and a poster) costs $12.75. Another package containing 13 comics (and a poster) costs $19.75. What is the linear equation that represents this situation?
The linear equation is y = x + 6.75.
500
An international food festival charges for admission and for each sample of food. Admission and 3 samples cost $5.75. Admission and 6 samples cost $8.75. What is the linear equation that represents this situation? Interpret the rate of change and the initial value.
The linear equation is y = x + 2.75. The rate of change means that each sample of food costs $1.00. The initial value means that the admission to the festival costs $2.75.