SLOPE of a Line from 2 Points

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Presentation transcript:

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 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 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 :

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

EXAMPLE 1 : Find the slope of the line that contains the points ( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

EXAMPLE 1 : Find the slope of the line that contains the points ( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

EXAMPLE 1 : Find the slope of the line that contains the points ( 2 , 5 ) and ( -1 , 4 ) x1 y1 x2 y2

EXAMPLE 2 : 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

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

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

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

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

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 )

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 )

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

SPECIAL slopes… Horizontal lines have zero slope.

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 )

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 )

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

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 )

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 )

Graphing slopes… 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 = STEPS : 1. Graph the given point

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

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

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