Slope What You'll Learn You will learn to find the slopes of lines and use slope to identify parallel and perpendicular lines. ? 1 – 4
There has got to be some “measurable” way to get this aircraft to clear such obstacles. Discuss how you might radio a pilot and tell him or her how to adjust the slope of their flight path in order to clear the mountain. If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree? Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 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. We measure the “change in height” required and divide that by the “horizontal change” required.
y x 10000
The steepness of a line is called the _____. slope Slope is defined as the ratio of the ____, or vertical change, to the ___, or horizontal change, as you move from one point on the line to another. rise run y x 10 -5 -10 5
The slope m of the non-vertical line passing through the points and is y x
The slope “m” of a line containing two points with coordinates Definition of Slope The slope “m” of a line containing two points with coordinates (x1, y1), and (x2, y2), is given by the formula
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 x (3, 6) rise = 6 - 1 = 5 units (1, 1) run = 3 - 1 = 2 units ? 6 & 7
Y = 3x-2 3=3 so the lines are parallel Slope Postulate 4 – 3 Two distinct nonvertical lines are parallel iff they have _____________. the same slope Y = 3x+4 Y = 3x-2 3=3 so the lines are parallel
? Y = 3x-2 Y = (-1/3) x +1 3* (1/3) = -1 so perpendicular Slope Postulate 4 – 4 Two nonvertical lines are perpendicular iff ___________________________. the product of their slope is -1 Y = 3x-2 Y = (-1/3) x +1 3* (1/3) = -1 so perpendicular ? 8 & 9