ZAMBALES NATIONAL HIGH SCHOOL

STRATEGIC INTERVENTION Material(linear function)

Prepared and Submitted:MAY PAMPUAN BUNDANG

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Least Mastered Skill

Objectives:

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Definition of Linear function f(x) = mx + b

A function is linear if and only if its equation can be written in the form y = mx + b or f(x) = mx + b, where m is the slope and b is the y-intercept of the line. This form is known as the slope-intercept form. The degree of the linear function is one. The graph is a non-vertical straight line.

Examples:1. Is y + 3x = 2 a linear function?Solve for y:

y + 3x = 2 The equation is in the form ax + by = c.y + 3x – 3x = -3x + 2 By APE, add – 3x to both sides of the

equation. y = - 3x + 2 The equation is now in the form y = mx + b

How will you

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Examples:

2. Is y = 2 a linear function?Since the equation can be written in the form y = mx + b or

f(x) = mx + b, where m = 0 and b = 2. Then, y = 2 is a linear function.

3. Is x2 – y + 1 = 0 a linear function?

Examples:1. Is y + 3x = 2 a linear function?Solve for y:

y + 3x = 2 The equation is in the form ax + by = c.y + 3x – 3x = -3x + 2 By APE, add – 3x to both sides of the

equation. y = - 3x + 2 The equation is now in the form y = mx + b

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Examples:

2. Is y = 2 a linear function?Since the equation can be written in the form y = mx + b or

f(x) = mx + b, where m = 0 and b = 2. Then, y = 2 is a linear function.

3. Is x2 – y + 1 = 0 a linear function?

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4. Is y(x + 6) = x(y + 3) a linear function?y(x + 6) = x(y + 3) Apply distributive property of

multiplication. xy + 6y = xy + 3x

xy + 6y + (-xy) = xy + 3x + (-xy) By APE, add – xy to both sides of the equations

6y = 3x

y =12 x

After simplifying, the equation is linear since it can be written in the form

y = mx + b, where m = 12and b = 0.

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Let us

Identify which of the following functions are linear.

1. y = 2x – 32. y = 3(x + 2) + 53. y = x(x – 4)4. y = -5x5. y = 3

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Given a Linear Function Ax +By = C, Rewrite in the Form f(x) = mx + b, a Slope-Intercept

Form and Vice Versa.

The standard form of linear equation Ax + By = C can be transformed to a linear function f(x) = mx + b called slope - intercept form, where m is the slope and b is the y-intercept.

What you will

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Example 1: Write 3y = -2x – 6 in the form f(x)= mx +b. Give the value of m and b.

Solution: 3y = -2x – 6

y = - 23 x – 2 By MPE, multiply 13 to both sides of the

equation

or f (x) = - 23 x – 2

How will you do

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Example 2: Write 5x + 2y – 5 = 6 in the form f(x)= mx +b. Give the value of m and b.

Solution: 5x + 2y – 5 = 6 Arrange the equation in the form ax + by = c

5x + 2y = 11 2y = -5x + 11 By APE, add – 5x to both sides of the

equation.

y = - 52 x + 11

2 By MPE, multiply 12 to both sides of the

equation

or f(x) = - 52 x + 11

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where m = - 52 and b =

112

Always remember that the numerical coefficient

of y should be one.

11standard form

ax + by = c

2x - y = -10standard form

ax + by = c

16x + 2y =

Example 3: Write y = 2x + 10 in the form ax + by = c.

Solution: y = 2x + 10

-2x + y = 2x + 10 + (-2x) By APE, add – 2x to both sides of the equation.

-2x + y = 10(-1)( -2x + y) = (10)(-1) By MPE, multiply -1

to both sides of the equation to make the leading coefficient positive.

Example 4: Write y = 112 - 8x in

standard form.Solution:

y = 112 - 8x By MPE,

multiply 2 to both sides of the equation to simplify the equation.

2y = 11 - 16x 16x + 2y = 11 - 16x + 16x By APE, add

16x to both sides of the equation.

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Let us

A. Transform the following equations to slope-intercept form.1. 5y + 10x = 202. 4y - x + 8 = 03. 5x – 2y = 14. x + y = 35. 4x – 4y = 10

B. Rewrite the following equations to standard form.

1. f(x) = -20x 2. y = -3x + 23. f(x) = 5x – 24. y = -5x + 4

5. y = 73 - 8x

Example 3: Write y = 2x + 10 in the form ax + by = c.

Solution: y = 2x + 10

-2x + y = 2x + 10 + (-2x) By APE, add – 2x to both sides of the equation.

-2x + y = 10(-1)( -2x + y) = (10)(-1) By MPE, multiply -1

to both sides of the equation to make the leading coefficient positive.

Direction: Identify which of the following functions are linear. Write LF if the function is linear and NLF if it is not.

____ 1. y = 2x _____ 6. y = 2(x -2)

____ 2. y = -5x + 10 _____ 7. f(x) = 3x + 6

____ 3. f(x) = -25x _____ 8. f(x) = 7(2x)2 + 3

____ 4. x = -7 + y _____ 9. y = 3 + x2

____ 5. xy = 10 _____10. f(x) = 3x − 2 13

activity 1: linear or not linear

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Direction: Write the following in slope-intercept form, y = mx + b. Determine the slope (m) and the y-intercept (b).

Equation y = mx + b m b1. 4y + 12x = 202. 2 x + 9y – 8 = 103. 4y + x + 2 = 04. 3x – y = 05. 8x – 2y = 66. 3x – 4y = 87. y + 5x – 3 = 08. 2y – 6x + 10 = 09. 7x + y + 4 = 3

10. y - 12x – 4 = 0

activity 2: see me like this

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Direction: Rewrite the following linear functions in standard form, Ax + By = C.

1. y = -4x + 2 ________________2. y = 3x – 5 ________________3. y = - x – 3 ________________4. y = 2x – 4 ________________5. y = 7x + 21 ________________6. y = 9 x + 8 ________________

7. y = -2 x – 52 ________________

8. y = -3x + 7 ________________9. y = 4x – 12 ________________

10. y = -2x + 34 ________________

activity 3: view me in another way

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Who said, “Genius is 1% inspiration, 99% perspiration”?

Transform the equations from standard form to slope-intercept form. Find the equation in the box below. Put the letter with the equation in the spot or spots for each question number.

1. 6x + 3y = 27 6. 2x – y = 3 11. -3x +2y = 42. y – 3x = -5 7. x – 2y = 6 12. -3x – 2y = 123. 3x + 2y = 8 8. 11x + 7y = 49 13. 7x + 2y = 3

4. 6x + 12 y = 3 9. 5x + 3y = 7 14. 2x – 8y = 0

5. -8x + y = 12 10. y – 2x = -4 15. 5x + 3y = 10

4 5 6 12 14 7 81 12 1 5119 3102 17

A y = -2x + 9 T y = -12x + 6 E y = 3x – 5

N y = - 32x + 4 O y = 8x +12 M y = 2x - 3

D y = 2x – 4 L y = 12 x – 3 S y = 32 x + 2

V y = - 117 x + 7 I y = - 5

3 x + 73 H y = - 3

2 x -

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Let us practice…1. LF 2. LF 3. NLF 4. LF 5. LF

Let us practice…A. B.1. y = -2x + 4 1. 20x + y = 0

2. y = 14 x – 2 2. 3x + y =

2

3. y = 52 x –

12 3. 5x – y =

2

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Activity 1: Linear or not linear

1. LF 6. LF2 LF 7. LF3. LF 8. NLF4. LF 9. NLF5. NLF 10. LF

Activity 2Equation y = mx + b m b

4y + 12x = 20 y = -3x + 5 -3 5

2 x + 9y – 8 = 10 y = - 29

x + 2 - 29

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4y + x + 2 = 0 y = - 14

x - 12

- 14

- 12

3x – y = 0 y = 3x 3 08x – 2y = 6 y = 4x - 3 4 -3

3x – 4y = 8 y = 34

x - 234

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Y+ 5x – 3 = 0 y = -5x + 3 5 32y – 4x + 2 = 0 y = 2x - 1 2 -17x + y + 4 = 3 y = -7x - 1 -7 -1

y - 12x – 4 = 0 y =

12 x + 1

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Activity 31. y = -4x + 2 ________________2. y = 3x – 5________________3. y = - x – 3________________4. y = 2x – 4________________5. y = 7x + 21________________6. y = 9 x + 8________________7. y = -2 x – ________________8. y = -3x + 7________________9. y = 4x – 12________________10. y = -2x + ________________

9x - y = - 8

4x + y = 23x - y = 5 x + y = -3 2x - y = 47x - y = -21

4x + 2y = -5

3x + y = 74x - y = 12

8x + 4y = 3

20Enrichment: THOMAS ALVA EDISON

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Obaña, Generoso G., and Edna R. Mangaldan. Making Connections in Mathematics IV. Manila, Philippines, 2004.

Abalos, Benjamin C., and Chrysel M. Abalos. Advanced Algebra, Trigonometry & Statistics. Philippines, 2003.