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**Parallel & Perpendicular Lines**

Comparing the slope of 2 lines determines if those lines are parallel, perpendicular, or just intersecting ( neither ). Parallel Lines – slopes are EQUAL Perpendicular lines – slopes are reciprocal AND opposite signs

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. ( 6 , 4 ) ( 2 , - 2 )

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. Use the slope formula : ( 6 , 4 ) ( x1 , y1 ) ( 2 , - 2 ) ( x2 , y2 )

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. Use the slope formula : ( 6 , 4 ) ( x1 , y1 ) ( 2 , - 2 ) ( x2 , y2 )

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. Use the slope formula : Answer ( 6 , 4 ) ( x1 , y1 ) Parallel lines have the SAME slope… ( 2 , - 2 ) ( x2 , y2 )

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. You could have also just counted the slope from the graph…start at one point and count… + 4 ( 6 , 4 ) + 6 ( 2 , - 2 )

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to the line on the graph. You could have also just counted the slope from the graph…start at one point and count… + 4 ( 6 , 4 ) + 6 ( 2 , - 2 ) Answer

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to Let’s solve for y and get the equation into y = mx + b form…

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to Let’s solve for y and get the equation into y = mx + b form…

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to Let’s solve for y and get the equation into y = mx + b form…

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to Let’s solve for y and get the equation into y = mx + b form… Here’s the slope…

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**Parallel & Perpendicular Lines**

Parallel Lines – slopes are EQUAL EXAMPLE : Find the slope of all lines parallel to Let’s solve for y and get the equation into y = mx + b form… So parallel slope would be the SAME … Answer Here’s the slope…

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the line on the graph. Use the slope formula : ( x1 , y1 ) ( - 6 , - 2 ) ( x2 , y2 ) ( - 1 , - 5 )

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the line on the graph. Use the slope formula : ( x1 , y1 ) ( - 6 , - 2 ) ( x2 , y2 ) ( - 1 , - 5 )

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the line on the graph. Use the slope formula : ( x1 , y1 ) To get the perpendicular slope, flip the fraction and change the sign… ( - 6 , - 2 ) ( x2 , y2 ) ( - 1 , - 5 )

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the line on the graph. Use the slope formula : ( x1 , y1 ) To get the perpendicular slope, flip the fraction and change the sign… ( - 6 , - 2 ) ( x2 , y2 ) ( - 1 , - 5 ) Answer

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the given equation.

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the given equation. Solve for “y” and get equation into y = mx + b form

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the given equation.

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs EXAMPLE : Find the slope of all lines perpendicular to the given equation. To get the perpendicular slope, flip the fraction and change the sign… Answer

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs Parallel Lines – slopes are EQUAL EXAMPLE : Are the given equations parallel, perpendicular, or neither.

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs Parallel Lines – slopes are EQUAL EXAMPLE : Are the given equations parallel, perpendicular, or neither. Compare the slopes : - not the same ( different signs ) - not reciprocal Therefore they are NEITHER

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs Parallel Lines – slopes are EQUAL EXAMPLE : Are the given equations parallel, perpendicular, or neither.

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs Parallel Lines – slopes are EQUAL EXAMPLE : Are the given equations parallel, perpendicular, or neither. Get both equations into y = mx + b form

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**Parallel & Perpendicular Lines**

Perpendicular lines – slopes are reciprocal AND opposite signs Parallel Lines – slopes are EQUAL EXAMPLE : Are the given equations parallel, perpendicular, or neither. Perpendicular Compare slopes… - not the same - they are reciprocal opposite signs

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