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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 EQUATIONThe slope, m, of a non-vertical line that contains the points P 1 ( x 1, y 1 ) and P 2 ( x 2, y 2 ) 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 ) x 1 y 1 x 2 y 2

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EXAMPLE 1 : Find the slope of the line that contains the points ( 2, 5 ) and ( -1, 4 ) x 1 y 1 x 2 y 2

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EXAMPLE 1 : Find the slope of the line that contains the points ( 2, 5 ) and ( -1, 4 ) x 1 y 1 x 2 y 2

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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 : 1.Choose a starting point 2.Move in a y - direction and count 3.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 : 1.Choose a starting point 2.Move in a y – direction and count 3.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 : 1.Choose a starting point 2.Move in a y – direction and count 3.Move in an x – direction and count +5

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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 : 1.Choose a starting point 2.Move in a y – direction and count 3.Move in an x – direction and count +5 +2

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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 P 1 ( 1, -3 ) P 2 ( 3, 2 )

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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 P 1 ( 1, -3 ) P 2 ( 3, 2 )

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

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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. P1 ( 2, -3 ) P2 ( 2, 4 )

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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 : 1.Graph the given point 2.Plot another point by following the given slope

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

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

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