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**Lines, Lines, Lines!!! ~ Standard Form**

Another equation of the same line.

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**What we Have Learned so far….**

Slope Intercept Form Where m is the slope and b is the intercept

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**What we Have Learned so far….**

Point-Slope Form Where m is the slope and are a point on the line.

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**We will use our prior knowledge of**

Slope-Intercept Form & Point-Slope Form To learn about the Standard Form of a Line: Ax + By = C

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**Standard Form The Standard Form of a Linear Equation is Ax + By = C**

Where A ≥ 0, & A and B are not both zero A, B, and C are integers whose greater common factor is 1.

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**Standard Form Notice that: x and y have exponents of 1**

The Standard Form of a Linear Equation is Ax + By = C Notice that: x and y have exponents of 1 x and y are not multiplied together x and y do not appear in denominators, exponents, or radicals

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**Examples of Standard Form**

These Equations are not in Standard Form: 1/2x + 2/3y = 6 12x – 36y = 10 5ix + 7py = -29 These Equations are in Standard Form: 2x + 5y = 7 x – y = - 10 1000x + 75y = 6

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Question: Is the equation 4x + 7y = -10 a linear equation? Explain why. This equation is a linear equation because it is in standard form with A = 4, B = 7, and C = –10. Is the equation 2xy = 4 a linear equation? Explain why. This equation is not a linear equation because x and y are multiplied by each other.

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**Writing an equation in Standard Form Ax + By = C**

y = 2/5x - 3 (5)y = (2/5x - 3)5 5y = 2x - 15 5y -2x = 2x -2x – 1 -2x + 5y = -15 -1(-2x + 5y = -15) 2x – 5y = 15 A= 2, B= -5, and C = 15

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**Writing an equation in Standard Form Ax + By = C Given A Point and a Slope**

Point (3,4) and m = 6 y - y1 = m(x - x1) Use Point-Slope Form y - 4 = 6(x - 3) Substitute the values y - 4 = 6x – 18 Use Distributive Property y = 6x Add Liked Terms y = 6x – 14 Slope-Intercept Form -6x + y = 6x – 6x – 14 Move the x value -6x + y = -14 Add Liked Terms -1(-6x + y = -14) Multiply times -1 6x – y = 14 Standard Form

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**Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4)**

First: Find the Slope between the two points Second: Use the Slope and the first point on the Point-Slope Form. Plug them in.

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**Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4)**

A = 3, B = 5 and C = 28

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**• • Steps to Graph Equations in standard form**

Write the equation in standard form Find x-intercept, by letting y = 0, solve for x, plot the point where x crosses the x-axis Find y-intercept, by letting x = 0, solve for y, plot the point where y crosses the y-axis Draw a line through the 2 points. Graph 2 x + 3 y = 12 Already using standard form: 2 x + 3y = 12 Let y = 0 2 x + 3(0) = 12 2 x = 12 x = 6 x-intercept is at ( 6 , 0 ) Let x = 0 2 (0) + 3 y = 12 3 y = 12 y = 4 y-intercept is at ( 0 , 4 ) • ( 0 , 4 ) 2 x + 3 y = 12 • ( 6 , 0 ) 13

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**Your Turn! How do you graph a line which is in standard form?**

Graph 3x - 4y = -12 x y 3 (3)0 - 4y = -12 -4 3x - (4)0 = -12 Graph the points and connect the dots

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Student Activity You will now receive a worksheet. Turn the worksheet in when completed.

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**Do Not Disturb Work In Progress**

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Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

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