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20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Coordinate Geometry Lesson: CG-L4 Slope Slope Learning Outcome B-4 CG-L4 Objectives: To calculate the slope of a line.

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20S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Coordinate Geometry Lesson: CG-L4 Slope So far, our coordinate geometry has focused on two points (distance between and midpoints). If you draw a line between the two points, another important mathematical attribute that can be studied is the slope, or slant of the line created. Slope can describe speed, acceleration, rates of change, costs, and many other things, depending on the situation, and is a key concept that we use a lot through Grades 10 – 12. Theory – Slope

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20S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Coordinate Geometry Lesson: CG-L4 Slope Slope, m, is defined as follows: m = Since rise = y 2 – y 1 (height between the two points) and run = x 2 – x 1 (horizontal distance between the two points), slope may be defined more exactly by the formula: m = A slope of a line determines the slant of a line. Formula - Slope

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20S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Coordinate Geometry Lesson: CG-L4 Slope Calculate the slope between the following sets of points using the slope formula. Sketch a line for each set of points. Theory – Calculate Slope (3,1) (5,6) (-2,4) (-1,-6) (3,-4) (7,-8) (-5,-5) (0,0) What do you notice about positive and negative slopes?

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20S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Coordinate Geometry Lesson: CG-L4 Slope Find the slope between the following sets of points using the slope formula. Sketch a line for each set of points. Theory – Calculate the Slopes (6,1) (2,1) (-3,-4) (-3, 2) (-2,-3) (7,-3) (4,-5) (4,0) Can you predict the slopes of the last two pairs without calculating or sketching them?

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20S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Coordinate Geometry Lesson: CG-L4 Slope On the following grid, draw a line through the point with the slope given. Sketch the slopes (-2,5) (-1,-4) (6,-3)-1 (5,0)3 (-6,-7) undefined

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20S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Coordinate Geometry Lesson: CG-L4 Slope How would you describe each of the following slopes? What angle would each slope form with the x-axis? Describe the slopes m = 0 m = undefined m = 1 0 < m < 1 1 < m m = -1

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20S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Coordinate Geometry Lesson: CG-L4 Slope A line passes through the points (2,5) and (-2,k). The slope of the line is 0.25. Find the value of k. Find k A line passes through the points (0,3) and (-6,k). The slope of the line is 2/3. Find the value of k.

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Lesson 5-1. The ___________ of a line is a number determined by any two points on the line. It is the ratio of the ___________ (vertical change) over.

Lesson 5-1. The ___________ of a line is a number determined by any two points on the line. It is the ratio of the ___________ (vertical change) over.

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