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?
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 slope-intercept form, which variable represents the initial/starting value? What is the mathematical name for it.
The variable b, called as y-intercept
200
Does this table represent a function?
Yes, it's a function!
200
What is the equation of this linear function?
y = 4x + 6.
200
Is the graph is linear or not? How do you know
No, it's a non-linear function! Because it failed the vertical line test
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?
y = 350x + 100.
300
Does this graph represent a function?
Yes, it's a function!
300
Write the equation of a line having a slope 1/2 and passing through (4,-7)
y=1/2 x - 9
300
How do you determine if a function is linear or non-linear from the table?
Calculate rate of change (or slope) for all the points in a table.
300
Find the x and y intercept of the equation below as a coordinate. Identify on which axis it is plotted.
6x - 12y = - 48
x intercept is (-8,0) plotted on x axis
y intercept is (0,4) plotted on y axis
300
A line has a slope of -5 and goes through the point (-4,-3). What is the linear equation that represents this line in point slope form?
y +3= - 5(x +4)
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 linear equation for a line that runs through the points (4, 10) and (12, 16)?
y = (3/4)x + 7
400
Rewrite the equation in slope intercept form.
3x+2y=-8
y = (-3/2)x - 4.
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, costing $12.75. Another package containing 13 comics, costing $19.75. What is the slope for the linear equation? What does the slope represent?
1) Slope = 1
2) The slope represents the cost per comic book
500
The value of a car decreases at a constant rate. After 3 years, the value of the car is $15,000. After 5 years the value of the car is $11,000.Write equation. interpret the y-intercept
y=-2000x+21000
The y-intercept is the initial value of the car