Straight Lines Objectives:

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Presentation transcript:

Straight Lines Objectives: D Grade Solve problems involving graphs, such as finding where the line y = x +3 crosses the line y = 2 C Grade Find the mid-point of a line segment, given two pairs of coordinates on the line Prior knowledge: Recognise and draw straight lines from equations of the form y = mx + c

Find the coordinates where the line y = 2 crosses x = 3 Straight Lines Find the coordinates where the line y = 2 crosses x = 3 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Draw the line y = 2 Draw the line x = 3 The lines cross at (3,2) The point of intersection

Straight Lines Now do these: Find the points of intersection of the following pairs of lines (use the grids on the paper supplied): 1. x = 1, y = -2 2. x = 4, y = -6 3. x = -6, y = -4 4. x = -6, y = 3 5. x = 7, y = 8 6. y = 0, x = 3 7. y = 5, x = -5 8. y = -2, x = -9 9. y = 1, x = 0 10. y = 10, x = 10 (1, -2) (4, -6) (-6, -4) (-6, 3) (7, 8) (3, 0) (-2, 5) (-9, -2) (0, 1) (10, 10) Can you see how to find the point of intersection without drawing the lines?

Find the coordinates where the line y = x + 1 crosses y = -2x - 2 Straight Lines Find the coordinates where the line y = x + 1 crosses y = -2x - 2 y Draw the line y = x + 1 10 9 Draw the line y = -2x - 2 8 7 The lines cross at (-1,0) 6 5 4 3 2 1 x 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Straight Lines Now do these: Find the points of intersection of the following pairs of lines (use the grids on the paper supplied): 1. y = x + 1, y = -x - 1 2. y = 2x - 1 , y = -3x + 9 3. y = 2x - 5 , y = x - 3 4. y = 3x - 4, y = -x + 4 5. y = 2x + 4 , y = -2x - 8 (-1, 0) (2, 3) (2, -1) (2, 2) (-3,-2)

(2, 3) (-1, 0) (2, 2) (2, -1) y = -x + - 1 y = - 3x + 9 y = x + 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = -x + - 1 (2, 3) (-1, 0) y = - 3x + 9 y = x + 1 y = 2x - 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = x + 3 (2, 2) y = x - 3 (2, -1) y = 3x - 4 y = 2x - 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Worksheet 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Worksheet 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10