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**Finding the equation of a line.**

POINT-SLOPE FORM y – y1 = m ( x – x1 )

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**Bell Work m = 8 , ( 7, 4 ) m = -10 , ( 6, -8 ) m = 5 , ( 9 , 3 )**

Using the point-slope form, find the equation of the line with the given conditions. Express your answer in y=mx + b. Having a slope of 3 and passing through the point ( 4, 5 ). Having a slope of -2 and passing through the point ( - 1, 6 ) m = 8 , ( 7, 4 ) m = -10 , ( 6, -8 ) m = 5 , ( 9 , 3 )

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Take Note If the given is the slope and a point on the line, we can use the point-slope form which is. y – y1 = m ( x – x1 )

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**What if the given slope is a fraction?**

Try this! Find the equation of the line having a slope of ¾ and passing through ( 2, 5 ).

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Solution Given : m = ¾ and passing through ( 2,5 ) y – y1 = m ( x – x1 ) y – 5 = ¾ ( x – 2 ) y – 5 = ¾ x – 6/4 y = ¾ x – 6/4 + 5 y = ¾ x + 7/2

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**Another solution y – y1 = m ( x – x1 ) y – 5 = ¾ ( x – 2 )**

m = ¾ and passing through ( 2, 5 ) y – y1 = m ( x – x1 ) y – 5 = ¾ ( x – 2 ) 4 ( y – 5 ) = 3 ( x – 2 ) 4y – 20 = 3x – 6 4y = 3x – 4y = 3x + 14 y = ¾ x + 7/ 2

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Try this! Find the equation of the line having the slope of ½ and passing through ( - 3, 4 )

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Try this! Find the equation of the line having a slope of 2/5 and passing through ( - 3, - 6 )

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Try this! Find the equation of the line having a slope of -2/7 and passing through ( - 1, - 4 )

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**Think – Pair - Share m = 2/3 ( 4, 7 ) m = ¼ ( 3, 1) m = 3/5 ( -2, 4)**

Find the equation of the line given the slope and a point. m = 2/3 ( 4, 7 ) m = ¼ ( 3, 1) m = 3/5 ( -2, 4) m = - 1/8 ( 3, -2) m = ½ ( 0, -23 )

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**Finding Slopes and y - intercepts from Equations**

y = mx + b

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Objectives: Change a linear equation to the form y = mx + b. Determine the slope of a line and the y-intercept from the given equations.

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**Thoughts to Ponder To determine the slope and**

y – intercept from a given equation, solve the equation for y in terms of x and express the resulting equation in the form y = mx + b. The coefficient of the x-term is the slope (m) and the constant term b represents the y-intercept.

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**Example: Find the slope of the line and y-intercept of 8x + y = 10.**

Solution: Given: 8x + y = 10 y = mx + b y = -8x + 10 Therefore the slope is -8 and the y-intercept is 10.

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Example Find the slope and y-intercept in the line 2x + 2y = 12 Solution: 2x + 2y = 12 2y = -2x y = -x + 6 Slope = -1 : y-intercept = 6

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Try this! Change 3y + 15 = 3x in y-form.

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Try this! Change 2y + 6x = 30 in y-form.

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Board Drill Change the following equations in the form y = mx + b. 10 x + y = 3

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2x – 2y = 6

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10x + 5y = 25

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14 x- 7y = -12

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2y – 4 = 35 – x

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**Seatwork 1. 9x + y = 18 2. 6x + 2y = 20 3. 3y + 5x = 2y + 2**

Change the following equations in the form y = mx + b, then determine the slope and y-intercept. Given Y-form slope Y-intercept 1. 9x + y = 18 2. 6x + 2y = 20 3. 3y + 5x = 2y + 2 4. 3x + 6y = -21 5. 2x + 3y = 15

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**Standard Form of Linear Equations**

Ax + By = C

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**Mathematical Concepts**

Standard Form Ax + By = C This is one of the two forms of a linear equation. The letters A, B, and C represent numbers. The numbers may not be fractions.

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Examples Change the equation y = -2x + 5 in Standard Form Given: y = -2x + 5 Solution: Just put all the variable terms on the left side of the equation. Note: x – term must comes first Answer: 2x + y = 5

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Examples 2. Change the equation y = 3x - 8 in Standard Form Given: y = 3x - 8 Solution: Just put all the variable terms on the left side of the equation. Note: the value of a should always be positive -3x + y = -8 -3x + y = -8 Multiply by -1 3x – y = 8

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**Examples 2/3 x + y = -7 Multiply by 3 2x + 3y = -21**

3. Change the equation y = -2/3x - 7 in Standard Form Given: y = -2/3 x - 7 Solution: Just put all the variable terms on the left side of the equation. Note: there must be no fractions in A, B, or C 2/3 x + y = -7 2/3 x + y = Multiply by 3 2x + 3y = -21

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Board Drill Write the following in standard form. y = 6x - 9

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Board Drill Write the following in standard form. 3x – 5 = 2y

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Board Drill Write the following in standard form. 7 = 2x – 3y

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Board Drill Write the following in standard form. y = -3/4x -10

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Board Drill Write the following in standard form. y = ½ x -7

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**y = -8x + 5 y = 10x + 2 3x – 6 = 7y y = 1/3 x – 5 y = -4/9 x + 3**

Seatwork Write the following equations in standard form. y = -8x + 5 y = 10x + 2 3x – 6 = 7y y = 1/3 x – 5 y = -4/9 x + 3

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**y = 8x - 13 Drills Group A: -3/5 x – 7y = 11 Group B Group C**

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Drills Group A: -4/7 x – 2y = 3 Group B y = 9x + 2 Group C y = -2x - 7

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**y = -1/2 x + 9 Drills Group A: -3/8 x – y = 7 Group B Group C**

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**Did you know that?...... Y-INTERCEPT = 𝑪 𝑩**

Using the Standard Form of Linear Equation we can also determine the value of the slope and y-intercept using the formula. SLOPE = −𝑨 𝑩 Y-INTERCEPT = 𝑪 𝑩

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**Change the equation in standard form then find the values of a, b, and c**

3x = 5y + 2 S. F 3x – 5y = 2 A = 3 B = -5 C = 2

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**Change the equation in standard form then find the values of a, b, and c**

y = 3x – 7 -3x + y = -7 Multiply by -1 3x – y = 7 Therefore: A = 3 B = -1 C = 7

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**Change the equation in standard form then find the values of a, b, and c**

3/4x = y – 7 ¾ x – y = -7 4 ( ¾ x – y = -7) 3x – 4y = -28 Therefore: A = 3 B = -4 C = -28

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**Think-Pair-Share 1. y = -4x + 5 2. y = 2x -7 3. 2x = 5 – 9y**

Complete the table below. Given S.F A B C m b 1. y = -4x + 5 2. y = 2x -7 3. 2x = 5 – 9y 4. y = 2/3x - 5 5. 7y = -4/9 x - 3

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Remember: Slope is also expressed as rise/run. Slope Intercept Form Use this form when you know the slope and the y- intercept (where the line crosses.

Remember: Slope is also expressed as rise/run. Slope Intercept Form Use this form when you know the slope and the y- intercept (where the line crosses.

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