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**SLOPE of a Line from 2 Points**

SLOPE – the measure of steepness, slant, or tilt of a line The letter m is used to represent slope in equations

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**SLOPE of a Line from 2 Points**

SLOPE – the measure of steepness, slant, or tilt of a line The letter m is used to represent slope in equations

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**SLOPE of a Line from 2 Points**

SLOPE – the measure of steepness, slant, or tilt of a line The letter m is used to represent slope in equations SLOPE EQUATION The slope, m , of a non-vertical line that contains the points P1 ( x1 , y1 ) and P2 ( x2 , y2 ) is :

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**EXAMPLE 1 : Find the slope of the line that contains the points**

( 2 , 5 ) and ( -1 , 4 )

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**EXAMPLE 1 : Find the slope of the line that contains the points**

( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

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**EXAMPLE 1 : Find the slope of the line that contains the points**

( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

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**EXAMPLE 1 : Find the slope of the line that contains the points**

( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

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EXAMPLE 2 : Find the slope of the line thru the given points.

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EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula

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EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula To count the slope from the graph : Choose a starting point Move in a y - direction and count Move in an x – direction and count

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EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula To count the slope from the graph : Choose a starting point Move in a y – direction and count Move in an x – direction and count

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EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula +5 To count the slope from the graph : Choose a starting point Move in a y – direction and count Move in an x – direction and count

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EXAMPLE 2 : Find the slope of the line thru the given points. +2 2 options : a ) count the slope from the graph b ) use the slope formula +5 To count the slope from the graph : Choose a starting point Move in a y – direction and count Move in an x – direction and count

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**Find the slope of the line thru the given points.**

EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula P2 ( 3 , 2 ) P1 ( 1 , -3 )

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**Find the slope of the line thru the given points.**

EXAMPLE 2 : Find the slope of the line thru the given points. 2 options : a ) count the slope from the graph b ) use the slope formula P2 ( 3 , 2 ) P1 ( 1 , -3 )

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SOME hints on slope… ( + ) positive slope : - always uphill from left to right - when counting, go up, and then right… OR down, and then left ( - ) negative slope : - always downhill from left to right - when counting : go down, then right… OR, up, and then left

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SPECIAL slopes… Horizontal lines have zero slope.

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**Horizontal lines have zero slope. **

SPECIAL slopes… Horizontal lines have zero slope. Y doesn’t change on a horizontal line. P1 ( -5 , 3 ) P1 ( 2 , 3 )

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**Horizontal lines have zero slope. **

SPECIAL slopes… Horizontal lines have zero slope. Y doesn’t change on a horizontal line. When you subtract your y – values in the slope equation, you get zero. P1 ( -5 , 3 ) P1 ( 2 , 3 )

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SPECIAL slopes… Vertical lines have no slope or an undefined slope.

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**Vertical lines have no slope or an undefined slope. **

SPECIAL slopes… Vertical lines have no slope or an undefined slope. X doesn’t change on a vertical line. P2 ( 2 , 4 ) P1 ( 2 , -3 )

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**Vertical lines have no slope or an undefined slope. **

SPECIAL slopes… Vertical lines have no slope or an undefined slope. X doesn’t change on a vertical line. When you subtract your x – values in the slope equation you get a zero. A zero in the denominator creates an undefined answer…you can not divide by zero. P2 ( 2 , 4 ) P1 ( 2 , -3 )

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Graphing slopes… EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m =

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Graphing slopes… EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m = STEPS : 1. Graph the given point

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Graphing slopes… EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m = STEPS : Graph the given point Plot another point by following the given slope

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**EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m =**

Graphing slopes… EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m = - 2 + 3 STEPS : Graph the given point Plot another point by following the given slope - negative slope so…down 2, then right 3

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**EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m =**

Graphing slopes… EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m = - 2 + 3 STEPS : Graph the given point Plot another point by following the given slope - negative slope so…down 2, then right 3 - plot your new point

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A) A(3,4), B(7,8) P(5,6). b) A(-5,-2), B(3,7) P(-1,2.5)

A) A(3,4), B(7,8) P(5,6). b) A(-5,-2), B(3,7) P(-1,2.5)

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