Straight Lines Objectives D Grade C Grade Solve

Straight Lines Objectives: D Grade C Grade Solve problems involving graphs, such as finding where the line y = x +3 crosses the line y = 2 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

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

Straight Lines Now do these: Find the points of intersection of the following pairs of lines (use the grids on the paper supplied): 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. x = 1, y = -2 x = 4, y = -6 x = -6, y = -4 x = -6, y = 3 x = 7, y = 8 y = 0, x = 3 y = 5, x = -5 y = -2, x = -9 y = 1, x = 0 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?

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

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

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

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

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