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### Linear Functions

- A
*linear*function is a function of the form f(x) = ax + b, where a and b are constants and a is nonzero. Its graph is a straight line. The x coordinate of the point at which the graph crosses the x axis is called the*x-intercept*. The*y-intercept*is defined similarly. Values of x for which f(x) = 0 are called*zeros*of f. - A
*linear equation*can be written in the form ax + by = c for some constants a, b, and c, where either a or b is not 0. If these constants are integers, the equation is in*standard form*. - The graph of a linear equation is a straight line.

### Linear Functions

Determine if the equation is linear:

− 5x + 4y = 22

− 5x + 4y = 22

yes

Determine if the equation is linear

14 = 2xy + 5y + 9

14 = 2xy + 5y + 9

no

Determine if the equation is linear

6s = 10 − [2/t]

6s = 10 − [2/t]

- t(6s) = ( 10 − [2/t] )t
- 6st = 10t − 2
- = 10t − 2

no

Determine if the following is a linear equation:

[4/x] + [5/y] = 0

[4/x] + [5/y] = 0

no

Find the intercepts of the equation:

[x/2] − [y/3] = 5

[x/2] − [y/3] = 5

- For the x intercept, let y = 0[x/2] − [0/3] = 5
- [x/2] − 0 = 5
- [x/2] = 5
- x = 10

x intercept = 10 - For the y intercept, let x = 0

[0/2] − [y/3] = 5 - 0 − [y/3] = 5
- − [y/3] = 5
- − y = 15
- y = 15

y intercept = 15

x intercept = 10

y intercept = 15

y intercept = 15

Find the intercepts of the equation:

[g/7] − [h/21] = 5

[g/7] − [h/21] = 5

- For the g intercept, let h = 0

[g/7] − [0/21] = 5 - [g/7] − 0 = 5
- [g/7] = 5
- g = 35

g intercept = 35 - For the h intercept, let g = 0

[0/7] − [h/21] = 5 - 0 − [h/21] = 5
- − [h/21] = 5
- − h = 105
- h = − 105

h intercept = 105

g intercept = 35

h intercept = 105

h intercept = 105

Find the intercepts of the equation:

[2x/9] − [y/4] = 12

[2x/9] − [y/4] = 12

- For the x intercept, let y = 0

[2x/9] − [0/4] = 12 - [2x/9] − 0 = 12
- [2x/9] = 12
- 2x = 108
- x = 54
- For the y intercept, let x = 0

[2(0)/9] − [y/4] = 7 - [0/9] − [y/4] = 7
- 0 − [y/4] = 7
- − [y/4] = 7
- − y = 28
- y = − 28

x intercept = 54

y intercept = −28

y intercept = −28

Find the intercepts of the equation

2x − 5y = 20

2x − 5y = 20

- For the y intercept, let x = 0
- 2(0) − 5y = 20
- − 5y = 20
- y = − 4
- For the x intercept, let y = 0
- 2x − 5(0) = 20
- 2x = 20
- x = 10

x intercept = 10

y intercept = −4

y intercept = −4

Determine the intercepts from the graph of the function

- Note the tick mark intervals

Intercept for the two equations is (1.5, − 0.5)

Determine the intercepts from the graph of the function

- Note the tick mark intervals

Intercept for the two equations is ( − 1, − 1[3/4])

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Linear Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Definition 0:07
- Standard Form
- Example
- Graph and Intercepts 2:39
- Example: Graph
- X-Intercept
- Y-Intercept
- Graphing Linear Equations 4:29
- Example
- Linear Functions 7:51
- Example
- Example 1: Linear 10:16
- Example 2: Linear Equation 12:58
- Example 3: Intercepts 14:23
- Example 4: Equation from Intercepts 16:47

1 answer

Last reply by: Edwin Wong

Thu Jun 27, 2013 5:33 PM

Post by Edwin Wong on June 27, 2013

At 9:44, you plotted the graph wrong.

2 answers

Last reply by: leo leyva

Mon Jul 15, 2013 2:49 PM

Post by Abel Gallegos on June 3, 2013

Dr. Eaton, is Ax+By=C the same as as Ax+By+C=0 form of the formula?

I Think both are used to show the form of lineal equations but I donÂ´t know if they are the same or if i should have Ax+By-C=0 instead,or just look to put the equation they way they ask me to. Thanks.

4 answers

Last reply by: Taylor Wright

Tue Jun 18, 2013 12:33 AM

Post by Erika Porter on May 3, 2013

On Exercise 2 if I put the problem 2/x-3/y=0 into standard form I get -3x+2y=0 which yields a straight line with coordinates such as (0,0),(1,1.5),(-1,-1.5),(2,3),(3,4.5).

However, I understand that substituting zero for either the x and y variables in the denominators is undefined, couldn't it just be that the line travels through the origin?

Thanks.