1. SLOPE OF A LINE When you hear the wordslopewhat comes to mind?

2. Slope of a Line The slope of a line measures the steepness of a line. You have probably heard teachers say rise over run. Rise means how many units you move up or down from point to point. On a graph that would be a change in the y-values. Run means how many units you move left or right from point to point. On a graph that would be a change in the x-values.rise slope runc 3. Positive Slope Note that a line y=0.5x+3 6with a positive 5 slope increases as43you read the2 graph from left to10right. -6-4 -20 2 4 6 Slope-Intercept Form c 4. Negative Slope y=-3x-26 Note that a line 4with a negative2slope decreases as -3 -2 -10 0 1 2 3-2 you read the-4graph from left to -6right-8 -10 Slope-Intercept Form c 5. Zero Slope y=0x+1 Note that a line1.2with a slope of1zero is horizontal0.8 0.6 as you read the 0.4 graph from left to0.2right0-3 -2 -1 0 1 2 3 Slope-Intercept Form c 6. Undefined SlopeX = -2 5 When a line is4 vertical, the slope is3 undefined. A2 vertical line cannot1 be written in Slope-0-2.5 -2 -1.5 -1 -0.50Intercept Form. -1 -2 -3c 7. Slope Formula Given Two Points You are now going to calculate the slope of a line and compare it to the Slope-Intercept Equations on the four previous slides. Given two points, x y and x y , calculate the slope.1, 12, 2 m = rise = change in y = x 2 - y1 run change in xy- x12 c 8. Positive Slope Given Two Points:A= - 4,1B= 2,4 m = 4 - 1 = 3 = 1 = 0.5 2 - -4 6 2Note that the slope of the line passing through points A and B is 0.5. Compare this to the first graph by clicking the arrow. 9. Negative Slope Given Two Points:A= - 2,4 B= 1,-5m= -5 - 4 = -9 = -3 1 - -2 3Note that the slope of the line passing through points A and B is -3. Compare this to the second graph by clicking the arrow. 10. Zero Slope Given Two Points: A= - 2,1B= 2,1m= 1- 1 = 0 = 02 - -2 4 Note that the slope of the line passing through points A and B is 0. Compare this to the thirdgraph by clicking the arrow. 11. Undefined Slope Given Two Points: A= - 2,4 B= 4,-7 m= -2 - 4 = -6 = undefined-2 - -2 0 Note that the slope of the line passing through points A and B is undefined. Compare this to the fourth graph by clicking the arrow. 12. Checking for UnderstandingThe Slope-Intercept Form of a line is y=mx+b where m is the slope of the line and b is the y-intercept of the line. Did you notice the relationship between the slopes that were calculated and the graphs of the equations? Now continue with the practice problems. 13. Practice Problems Given the equation, what is the slope of the line? y 2x 7 A) 7 C) 3 3 2B) 2 D) X3 14. That response is incorrect, the correct2 response is 3 . Remember that when an equation is in Slope-Intercept form, y=mx+b, the slope is the coefficient of x. Dont be discouraged! Lets try another problem. 15. That is Correct! 16. Practice Problems Calculate the slope of the line that passes through the given points.A= -5,2 A) -1C) 5B= 4,-7 B) 5 D) 995 17. That is incorrect. The correct response is A. Refer back to slide 9 if you need to review how to calculate the slope of a line using the slope formula. -7 - 2 -9m= = = -1 4 - -5 9 18. That is correct! 19. Determine the slope of the line fromthe given graph. y-axis4 1 3 A) -2 B) 22 11 0C) 2D) -2 -1-1 0 1 2 3 4 2 -2 -3 -4 -5 -6 20. That is correct! 21. That is incorrect. If you start at the point (0,-3) and move to the point(1,-1), the movement was 2 units up and 1 unit right which means the slope is 2 which is 2. 1 22. ConclusionToday you have learned to find the slope of a line by reading a graph, using the slope formula, and by knowing that in the slope-intercept formula, m is the slope. In our next lesson, we will continue our study of linear functions. Cheers! 23. Positive Slope Note that a line y=0.5x+3 6with a positive 5 slope increases as43you read the2 graph from left to10right. -6-4 -20 2 4 6 Slope-Intercept Form 24. Negative Slope y=-3x-26 Note that a line 4with a negative2slope decreases as -3 -2 -10 0 1 2 3-2 you read the-4graph from left to -6right-8 -10 Slope-Intercept Form 25. Zero Slope y=0x+1 Note that a line1.2with a slope of1zero is horizontal0.8 0.6 as you read the 0.4 graph from left to0.2right0-3 -2 -1 0 1 2 3 Slope-Intercept Form 26. Undefined SlopeX = -2 5When a line is4 vertical, the slope is3 undefined. A2 vertical line cannot1 0 be written in Slope- -2.5 -2 -1.5 -1 -0.50-1 Intercept Form. -2 -3 27. Nice work!