Slope of a Line Prepared by Gladys G. Poma

Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells us how much the line rises from one point to another located one unit to the right. 1 unit Rise Examples : 1 unit Slope = 2 Slope = 1 Slope = ½ 0r units 1 unit ½ or 0.5 of a unit 2

A. Using only the concept of slope and a ruler, find the slope of the following lines: B.Using only the concept of slope and a ruler draw lines with the following slopes: EXERCISES : 1) Slope = Slope = 3Slope = ¼ 0r

A. Using the concept of slope and the grid find the slope of the following lines: B. Using the concept of slope and the grid draw lines with the following slopes: Slope = 2) Slope = 2.5 Slope = Slope = 2 4

1 unit Slope = 2 or +2 2 units going up Example: Positive SlopeNegative Slope 2 units going down or -2 1 unit Slope = _ _ Positive: When the line actually rises or goes up. Negative: When instead of rising, the line goes down. Moving left to Right 5

1. Indicate the sign of the slope for each line shown below. 2. Find the slope of the following lines. Slope = EXERCISES : Slope = 3. What is the slope of the line in the graph? Choose the best answer. a)½ b)2 c)-2 d)- ½ e)1/3 Use a ruler 6

The slope indicates rise per unit of horizontal right movement and this value is the same everywhere along the line, because the line is straight. Then, if we move more than one unit to the right, the rise will be proportional. That is why, to find the slope we can use any two points on the line and find the ratio of their vertical distance to their horizontal distance. Definition : y x = Horizontal Distance Vertical Distance Y2 – Y1 == X2 – X1 Slope 1 unit Y2 Y1 X1 X2 GED Formula Then, there are two ways to find the slope of a line:  Use a graph to find x and y and find the ratio; or  Use the formula. 7

x y Steps: 1.- Use the graph to choose a x and a y with lengths that have an exact number of units. 2.- Slope = y / x In the graph: x = 4 and y = 5, then the Slope = x y = 5 4 Example : 8

EXERCISES : Find the slope of each line (From the book: GED Mathematics. Steck-Vaughn) Slope = y x x x y y x y The line that passes through the points: (1,-3) and (0,1). y x Slope = Note: Draw the line and find the slope using the graph 9

Y2 Y1 X1X2 Point 2 Point 1 Point 1 = (X1,Y1) Point 2 = (X2,Y2) If the coordinates of two points are given, we do not need the graph to use the Slope Formula. Formula : Point 1 = ( 2, 4 ) and Point 2 = ( 9, 8 ) Y2 – Y1 X2 – X1 X1Y1 Example : In the graph : X2Y2 Then, Y2 – Y1 X2 – X1 Slope = = 8 – 4 9 – 2 =

EXERCISES : Find the slope of the line that passes through each pair of points. (From the book: GED Mathematics. Steck-Vaughn) x y 1. (4,5) and (3,- 4) 4. The points are shown in the graph 2. (- 3,- 3) and (- 2,0) Use the formula to solve. Suppose you do not know the concept of a slope and the graph method, only the formula. 3. (- 4,3) and (5,3) 11

1)Two teams : Both teams solve the same exercise, but each team uses a different method. Students work in pairs or independently. The student who finishes first in each team writes the solution on the board. The team/method that finishes first wins. Data: Coordinates of two points 2)Same as part 1, but switch methods between teams. Data: Coordinates of two points 3) Similar to part 1, but now each person chooses his or her favorite method. If everybody chooses the same method, then the students that finish first in parts 1 and 2 must use the other method. Data: Coordinates of two points Objective : Compare the two given methods to find the slope: Graph and Formula. The student will work with both methods and choose which one they like better. At the end, discuss which method won more times and why. 12

 The slope of any horizontal line is 0.  A vertical line has no slope.  All lines with the same slope are parallel.  If we have the equation of a line written in the form: y = mx + b, where m and b are numbers, then m is the slope of the line. Examples : 1) The line with equation y = 3x - 4 has slope 3. 2) The line with equation y = -x + 5 has slope