Functions
Linear Functions
Linear or Non-Linear Functions
Writing Linear Equations
Equations
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 k.
100
A square has an area of 36 square feet. A second square has an area of 144 square feet. How much greater is the side length of the second square than the side length of the first square?
6
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 equation y = 1,500 – 30x can be used to estimate the number of cars in a parking lot x minutes after the end of a concert. What is the meaning of the slope of the linear model?
About 30 cars leave the parking lot every minute after the concert ends.
300
Is this a function?
Yes! Every input has exactly one output!
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
What is the value of x in the equation shown below?
1/2(2x+6)=5x+15-3x
-12
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 approximate distance between the points (–2, 7) and (4, –3)?
11.7
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
Two companies sell shirts. x The first company charges $18 per shirt plus an additional $12 for shipping. x The second company charges $20 per shirt plus an additional $4 for shipping. How many shirts are in an order that would cost the same from both companies?
4