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Slope

The document discusses slope and how to calculate it. It defines slope as the rate of change of a line and provides the formula slope=rise/run. It then explains how to find the slope of a line graph by picking two points and calculating rise over run. Finally, it demonstrates how to find the slope of a line given two points or from a table of x-y values using the same rise over run formula.

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M. Pickens 2006 Slope
M. Pickens 2006 Objectives • To learn what slope is • To learn what a line looks like when it has positive, negative, zero or undefined slope • To learn how to find the slope of a graph • To learn how to find the slope given 2 points • To learn how to find the slope of a table
= D (change in y) M. Pickens 2006 What is Slope? Slope is the rate of change of a line slope = rise x run slope y D (change in x) slope = y - y 2 1 x - x 2 1
What does the line look like when… • You have positive slope? • You have negative slope? M. Pickens 2006 • You have zero slope? • You have NO slope?
M. Pickens 2006 Slope Mountain Ski Resort Positive slope, + work Negative slope, - work Zero slope is zero fun! NO slope. Oh No!!!! T. Merrill 2005
M. Pickens 2006 Lets Cheer Positive, Negative Zero NO X-Axis Y-Axis Go, Go, Go
What Type of Slope is M. Pickens 2006 Shown? Positive Slope Negative Slope Zero Slope No Slope/Undefined
M. Pickens 2006 Slope of a Graph • When slope is positive or negative we need to find the actual value of the slope or rate of change • On a graph we find slope using the formula slope = rise run How far up or down it changes How far left or right it changes
= 2 M. Pickens 2006 Slope of a Graph 1.First pick two points on the line The points need to be where the lines cross so they are integers 2. Then find the rise and run 3. Determine if the slope of the line is positive or negative Rise = 2 Run = 3 slope = rise run 3
= 10 = 5 M. Pickens 2006 Slope of a Graph 1.First pick two points on the line The points need to be where the lines cross so they are integers 2. Then find the rise and run 3. Determine if the slope of the line is positive or negative Rise = 10 Run = 2 slope = rise run 2
Slope of a Graphed Line RISE 1 - 4 = - 0 = 4 - 8 = - 3 2 M. Pickens 2006 Find the slope of each line below Find the slope of each line below x y Slopes: = RUN 1 4 4 4 0 6 1 2 4 = undefined 0
Slope of line through 2 points • To find the slope of a line through 2 given points we use the formula slope = y - y 2 1 x - x • For example, Find the slope of a line that goes through (--3, 3 5) 5 and (2, 2 18) 18 M. Pickens 2006 2 1 X1 y1 X2 y2 slope = y - y 2 1 x - x 2 1 = 13 5
Given two points on a line, find the slope: 1. (9, 2), (8, -7) = - = 9 - - 3 M. Pickens 2006 2. (-4, 4), (-7, 2) - 7 4 2 4 2 4 3. (5, -1), (9, -4) y y 2 1 x 2 x 1 rise run - - - 8 9 7 2 - 1 - y - y - 2 1 x 2 x 1 = - - - = 2 = = 2 - - - 9 5 4 1 - = - - - - + 3 7 4 = - + 9 5 4 1 - 4 X1 y1 X2 y2 = 9 X1 y1 X2 y2 X1 y1 X2 y2 3
Given two points on a line, find the slope: 4. (5, 2), (1, 0) = - = 2 - 1 3 Undefined, NO slope = 1 2 2 0 = 0 M. Pickens 2006 5. (3, -3), (3, -1) - - - 3 3 1 3 - + 6. (-4, -2), (4, -2) y y 2 1 x 2 x 1 rise run - - 1 5 0 2 - 4 - y - y - 2 1 x 2 x 1 = - = 2 = = - - - 4 4 2 2 - - - 0 3 3 = - + 4 + 4 8 X1 y1 X2 y2 2 X1 y1 X2 y2 X1 y1 X2 y2
= + 4 2 - = 6 = 3 M. Pickens 2006 Slope of a Table • In a table we can use the same formula. Pick any two pairs in the table for coordinates x y -4 -17 1 -2 3 4 8 19 10 25 slope = y - y 2 1 x - x 2 1 Pick any two rows. If it is linear it will be the same no matter which two rows you pick x1 x2 y1 slope = - - y2 3 1 4 2 - 3 1 2
slope = y - y 2 1 x - x = - 3 2 - - - = - 3 2 - + = 1 M. Pickens 2006 Slope of a Table • Find the slope for each table below x y -3 4.25 -1 2.75 0 2 1 1.25 5 -1.75 x y -8 2 -6 3 -3 4.5 -1 5.5 0 6 slope = y - y 2 1 x - x 2 1 = - 2.75 4.25 - - - 1 3 = -1.5 2 = -0.75 = - 3 4 2 1 6 8 6 8 2
slope = y - y 2 1 x - x = - - - 8 8 - - - = - + 8 8 - + = 0 = 0 M. Pickens 2006 Slope of a Table • Find the slope for each table below x y slope = y - y 2 1 x y -10 17 x - x 2 1 -3 -8 -5 10 = 10 - 17 -1 -8 -1 4.4 - 5 - - 10 0 -8 5 -4 = - 1 -8 10 -11 4 -8 10 17 - + 5 10 = - 7 5 2 1 1 3 1 3 2
slope = y - y 2 1 x - x 2 1 M. Pickens 2006 Conclusion • Slope is: the rate of change of a line slope = rise run • Describe the slope of each of the following Negative slope Undefined/ No slope Positive slope Zero/0 slope