1. 6.1 LINEAR FUNCTIONS

2. Make a table and graph the ordered-pair solutions for this equation.
The equation y = 2x gives the number of inches of snow y that fell in x hours.
Make a table and graph the ordered-pair solutions for this equation.
What pattern do the points form?
Why? x
Hours 1 2 3 4 5 6 y
Inches 8 10 12

3. A linear function is a function whose graph is a straight line
A linear function is a function whose graph is a straight line. However the line can't be vertical, since then we wouldn't have a function. A linear function can be described by a linear equation. A linear equation is any equation that can be written in standard form: Ax + By = C where A, B, and C are real numbers and A and B are not both zero.

4. Examples of linear equations:
x + 3y =7
2x – 5y + 8 = 0
Notice the x and y both have an exponent of 1
x and y are not multiplied together
x and y do not appear in a denominator, exponent, or radical

5. Examples of equations that are Not linear:
xy + 7 = x + y
x + 3y2 = 6 

6. Tell whether each equation is linear
Tell whether each equation is linear. If so, graph the function represented by the equation. 1. x = 2y + 4
Domain
(x)
Range
(y)

7. 2. xy = 4 3. y = x2 + x + 1

8. While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (every input must have only one output).
Any equation of the form y = (constant) will give us a linear function.
Ex:
y = 4
y = -9
y = 1 2

9. However, any equation of the form x = (constant) is a linear equation but does not describe a function.
(Remembering the absolute nonsense words "yunction" and "xquation" should help you keep things straight.)
Here is why?

10. Make a table of values and graph y = 2.
Here is why?
Make a table of values and graph y = 2.
Domain
(x)
Range
(y) -1 2 1
It is a straight line (linear) and passes the vertical line test (function).

11. Domain (x) Range (y) 1 -1 Make a table of values and graph x =1
Straight line (linear), but it fails the vertical line test-not a function.

12. 2. xy = 4 3. y = x2 + x + 1

13. Write a linear equation in the form Ax + By = C for the given values of A, B, and C.
Then simplify the equation. Tell whether the equation represents a horizontal line, vertical line, or neither.
4. A = 2, B = 2, C = 2
5. A = 0, B = 5, C = 0
6. A = −8, B = 0, C = 8

14. charge for a 6-hour job? Does either consultant charge according to a
The solid and dashed graphs below show how two
consultants charge for their daily services.
7.How much does each
charge for a 6-hour job?
Does either consultant
charge according to a
linear function?

15. The solid and dashed graphs below show how two
consultants charge for their daily services.
 9. For which length of job do
A and B charge the same
amount?

16. 10. Gloria and Jane work for the same accounting firm.  
10. Gloria and Jane work for the same accounting firm.
Gloria gets paid $75, 000 a year. Jane gets paid $2000 plus $70 per hour.
Write an equation for each person that shows the relationship between the annual salary y and the number of hours x that they work.