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 slope-intercept form, which variable represents the initial/starting 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
What is the slope of the line that passes through the points (-8,-6) and (4,3)
The slope is
+3/4
200
The starting fee at a sports gym is $50 and every class costs $10. What is the linear equation of the cost?
The linear equation is y = 350x + 100.
300
Does this graph represent a function?
Yes, it's a function!
300
What is the use of The Vertical Line Test
to determine if a graph is a function or not
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 3 and goes through the point (0,6). What is the linear equation that represents this line?
The linear equation is y = 3x +6
300
A line has a slope of -5 and goes through the point (0,-3). What is the linear equation that represents this line?
The linear equation is
y = - 5x - 3.
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 (3, 11) and (0, 7)?
It is y = (3/4)x + 7
400
What is the linear equation for a line that runs through the points (0, -1) and (9, 5)?
The linear equation is y = (-3/2)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
In a store, 6 comics cost $12.75, and 13 comics cost $19.75. What is the slope for the linear equation? What does the slope represent?
Hint: ''x'' is the number of comics, and ''y'' is the total cost.
1) Slope = 1
2) The slope represents the cost per comic book
500
The starting fee at a sports gym is $50 and every class costs $10. What is the total cost after 12 classes?
The linear equation is y = 350x + 100.
After 12 classes, y = 10(12) + 100 = $220