Slope You will learn to find the slopes

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Slope You will learn to find the slopes of lines and use slope to

Slope You will learn to find the slopes of lines and use slope to identify parallel and perpendicular lines. 1 – 4

There has the got to bechange some “measurable” to will get not this make

There has the got to bechange some “measurable” to will get not this make aircraft If the pilot doesn’t something, heway / she it Consider options: to clearfor such obstacles. home Christmas. Would you agree? 1) Keep the same slope of his / her path. Discuss you might radio a pilot and tell him or her how to Not ahow good choice! adjust the slope of their flight path in order to clear the mountain. 2) Go straight up. Not possible! This is an airplane, not a helicopter.

Fortunately, there is a way to measure a proper “slope” to clear the obstacle.

Fortunately, there is a way to measure a proper “slope” to clear the obstacle. We measure the “change in height” required and divide that by the “horizontal change” required.

y 10000 0 0 10000 x

y 10000 0 0 10000 x

Slope slope The steepness of a line is called the _____. Slope is defined

Slope slope The steepness of a line is called the _____. Slope is defined as the ratio of the ____, run or rise or vertical change, to the ___, horizontal change, as you move from one point on the line to another. 1 0 y 5 -10 -5 5 -5 -10 1 0 x

Slope The slope m of the non-vertical line passing through the points and is

Slope The slope m of the non-vertical line passing through the points and is y x

Slope The slope “m” of a line containing two points with coordinates (x 1,

Slope The slope “m” of a line containing two points with coordinates (x 1, y 1), and (x 2, y 2), is given by the formula Definition of Slope

Slope The slope m of a non-vertical line is the number of units the

Slope The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. y (3, 6) rise = 6 - 1 = 5 units (1, 1) x run = 3 - 1 = 2 units 6 & 7

Slope Two distinct nonvertical lines are parallel iff they have the same slope _______.

Slope Two distinct nonvertical lines are parallel iff they have the same slope _______. Postulate 4– 3 Y = 3 x+4 Y = 3 x-2 3=3 so the lines are parallel

Slope Two nonvertical lines are perpendicular iff the product of their slope is -1

Slope Two nonvertical lines are perpendicular iff the product of their slope is -1 ______________. Postulate 4– 4 Y = 3 x-2 Y = (-1/3) x +1 3* (1/3) = -1 so perpendicular 8 & 9