2-3 Slope Slope is “the change in y over the change in x” (vertical over horizontal). rise / run is the ‘m’ in y = mx + b.

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Presentation transcript:

2-3 Slope Slope is “the change in y over the change in x” (vertical over horizontal). rise / run is the ‘m’ in y = mx + b.

Slope Formula m=

Slope If a line rises from left to right (leans), x y If a line rises from left to right (leans), it has a positive slope. If a line falls from left to right, it has a negative slope. x y

Slope If a line is vertical, it has an undefined slope. (Remember x = #). If a line is horizontal it has a slope equal to 0. (Remember y = #). x y x y

Find the Slope To find the slope of this line we will use rise/run. Pick either point. We find the rise by counting up (+) or down (-). Rise is 3 up from a or -3 down from b. y b x a

Find the Slope To find the run, we count right (+) or left (-). If you started from b, your run will be left -2, if you started at a, your run will be right 2. x y b a

Find the Slope So if you started with b, your slope would be -3/-2. x y So if you started with b, your slope would be -3/-2. If you started with a, your slope would be 3/2. Are these the same? Yes!! The slope of the line is 3/2. b a

Find the Slope x y x y m = m =

Find the Slope x y x y m= undefined m = 0

Find the Slope of the Line Given the points (5, 1) & (6, 4) m = = = 3 Given the points (-6, -2) & (-1, 0) m =

Parallel Lines What do you know about the slope of parallel lines? Parallel lines have the SAME SLOPE! What is the slope of the line parallel to y = -2x + 4? m = -2

Perpendicular Lines What do you know about the slope of perpendicular lines? Perpendicular lines have slopes that are opposite reciprocals! What is the slope of the line perpendicular to y = -2x + 4? m = 1/2

Graphing a Line Given a Point & Slope Graph a line though the point (2, -6) with m=2/3 Graph (2, -6) Count up 2 for the rise, and to the right 3 for the run Plot the point, repeat, then connect x y

Graphing Lines Graph the line perpendicular to y = 2x + 3 that goes through the point (-2, 3). The slope of the line is 2 so the slope of the perpendicular line is -1/2. m = -1/2 b = 3

Graphing Lines m = - ½ b = 3 Plot y-intercept (b) Use the slope to find two more points Connect x y

Graphing Lines Graph the line parallel to x = -1 that goes through the point (3, -3). The slope of the line is undefined so the slope of the parallel line is undefined.

Graph the Line (3, -3) m = undefined x y

Homework pg 72 15-27 odd