The Slope Formula Finding The Slope Between Two Points © 2011 The Enlightened Elephant

Teacher Tips The next slide visually explains the slope formula. When viewing the next slide: To help explain how to find “vertical change” the yellow line and the red line will appear on the graph first. The yellow line represents the length of y2 and the red line is y1. Ask students if they can tell you the length of the yellow line and the red line and/or explain their lengths using the y-axis as a reference. The red line will overlap onto the yellow line so that students can see (and you can explain) that if you remove the red line section (length y1) from the yellow line (length y2) the resulting length will be “vertical change” To help explain how to find “horizontal change” the orange line and the purple line will appear on the graph next. The orange line represents the length of x2 and the purple line is x1. Ask students if they can tell you the length of the orange line and the purple line and/or explain their lengths using the x-axis as a reference. The purple line will overlap onto the orange line so that students can see (and you can explain) that if you remove the purple line section (length x1) from the blue line (length x2) the resulting length will be “horizontal change” © 2011 The Enlightened Elephant

Horizontal Change Vertical Change Slope = Vertical Change Horizontal Change = Slope Vertical Change Horizontal Change Vertical Change Horizontal Change To Find Vertical Change To Find Horizontal Change What are the lengths of the yellow and red lines? What are the lengths of the orange and purple lines? © 2011 The Enlightened Elephant

Horizontal Change Vertical Change Example Find the slope between (9, 9) and (5, 3) Slope = Vertical Change Horizontal Change = == © 2011 The Enlightened Elephant

Slope = Vertical Change Horizontal Change (4,2) (2,-1) 1. Find the slope between (2, -1) and (4, 2) == You Try It! = Slope = Vertical Change Horizontal Change (-5,1) (-2,-3) 2. Find the slope between (-5, 1) and (-2, -3) == = © 2011 The Enlightened Elephant

Game Directions Have students get into pairs (or if you have an odd number you can have one group of three). Print out slide #9 and make enough copies for each pair of students to have one copy between them. Each pair of students needs a different color writing utensil (I use two different colored crayons), an individual whiteboard with a marker or scratch paper and pencil. Show the first problem from the problem set for the game. Students calculate the slope and whoever finds it and circles it first gets the point. Show the solution and the next problem (I usually work out the first few on the board after students try them). Whoever has the most colored circles at the end of the game has the most points and thus wins. © 2011 The Enlightened Elephant

Let’s play a GAME to practice! Directions Calculate the slope between the two given points, find it and circle it on your paper faster than your opponent! © 2011 The Enlightened Elephant

1. (19,-16) and (-7, -15) -1/26 2. (-4, 7) and (-6, -4) 11/2 3. (17, -13) and (17, 8) undefined 4. (3, 0) and (-11, 15) 15/14 5. (6, -10) and (-15, 15) -25/24 6. (3, -20) and (5, 8) (-19, 12) and (-9, 1) -11/10 8. (6, -12) and (15, -3) 1 9. (1, -19) and (-2, -7) (19, 3) and (20, 3) (20, 8) and (9, 16) -8/ (9, 3) and (19, -17) -2 Find the slope between the two points. m= © 2011 The Enlightened Elephant

0 15/ /2 -2/ /10 -3/19 -1/32 undefined -25/ /26 -8/ /5 4/11 -1/5 © 2011 The Enlightened Elephant Directions Calculate the slope between the two given points, find it and circle it faster than your opponent!

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