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20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Writing Equations of Lines Learning Outcome B-4 CG-L6 Objectives: To determine the slope y-intercept form of a line given various inputs.

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20S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Plot the following equations in Winplot, on the same screen. These equations are all in the form y = mx. What is m? Theory – Deriving the Equation of a Line

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20S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Plot the following equations in Winplot, on the same screen. These equations are all in the form y = mx + b (where m is 1). What is b? Theory – Deriving the Equation of a Line

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20S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Predict the line for each equation shown. State slope & y-intercept for each case. Example 1 – Two Points

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20S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines The Slope, Y-Intercept Form of the Line describes a straight line with slope of m and y-intercept b. A Line is just a collection of points. The coordinates (x,y) of each point on the line will work in the equation (make the equation true). Find three points on each line shown: Example 1 – Two Points

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20S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Determine if the point is on the line. Example 1 – Two Points (-1,1) (0,-2) (50,-49)

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20S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines The equations of horizontal and vertical lines look a little different. We can understand their equations by considering each to be collections of points, at a common distance from an axis. Horizontal Lines Vertical Lines Example 2 – Two Points (Special Case)

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20S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Write the equation for each line. Example 3 – Two Points (Special Case)

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20S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Write the equation for each line. Example 3 – Two Points (Special Case)

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20S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Write equations in the form y = mx + b for the following straight lines. passes throughslopey-interceptequation 41 -1/6-3 (1,3)2 (0,3)-1/2 (-3,-2)(0,1) (4,3)-1 (-1,0)0 (5,6)undefined Example 4 – Given Slope, One Point

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20S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Coordinate Geometry Lesson: CG-L6 Writing Equations of Lines Write equations in the form y = mx + b for the following straight lines. (Hint: use the slope formula to find m, then substitute either point to find b) passes throughand (-1,-2)(1,2) (-4,-4) (2,-1) Example 4 – Given Slope, One Point

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