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Slope

Slope. CG-L4 Objectives: To calculate the slope of a line. Learning Outcome B-4.

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Slope

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  1. Slope CG-L4 Objectives:To calculate the slope of a line. Learning Outcome B-4

  2. 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

  3. Slope, m, is defined as follows: m = Since rise = y2–y1 (height between the two points) and run = x2–x1 (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

  4. Calculate the slope between the following sets of points using the slope formula. Sketch a line for each set of points. (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? Theory – Calculate Slope

  5. Find the slope between the following sets of points using the slope formula. Sketch a line for each set of points. (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? Theory – Calculate the Slopes

  6. On the following grid, draw a line through the point with the slope given. (-2,5) (-1,-4) (6,-3) -1 (5,0) 3 (-6,-7) undefined Sketch the slopes

  7. How would you describe each of the following slopes? What angle would each slope form with the x-axis? m = 0 m = undefined m = 1 0 < m < 1 1 < m m = -1 Describe the slopes

  8. A line passes through the points (2,5) and (-2,k). The slope of the line is 0.25. Find the value of 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. Find k

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