1. Gradient and Intercept Geometry

2. Copy and complete the tables on the next slides. [Reminder ; The equation of a straight line is given by y = mx + c where m = gradient and the line cuts the y axis at (0,c) ]

3. Equation of the lineGradient m Point where the line cuts the y axis y = 2x + 72(0,7) y= x - 51(0,-5) y = 3x y = 4x - 1 y = -3x -6 y = -x -4 y= 5x + 8 y = 2.5x +1 y = -2x -3 Table 1

4. Equation of the lineGradient m Point where the line cuts the y axis y = 2x + 72(0,7) y= x - 51(0,-5) y = 3x 3(0,0) y = 4x - 1 4(0,-1) y = -3x -6 -3(0,-6) y = -x -4 (0,-4) y= 5x + 8 5(0,8) y = 2.5x +1 2.5(0,1) y = -2x -3 -2(0,-3) Table 1 - solutions

5. Equation of the lineGradient m Point where the line cuts the y axis y= 3x - 5 y = 3.5x y = 2 – 4x y = -2 – 2x y = 1.5x y = 2.5x + 4 y = -2x y = 4 + x y = -2.2x – 8.9 Table 2

6. Equation of the lineGradient m Point where the line cuts the y axis y= 3x - 5 3(0,-5) y = 3.5x 3.5(0,0) y = 2 – 4x -4(0,2) y = -2 – 2x -2(0,-2) y = 1.5x 1.5(0,0) y = 2.5x + 42.5(0,4) y = -2x-2(0,0) y = 4 + x1(0,4) y = -2.2x – 8.9 -2.2(0,-8.9) Table 2 - solutions

7. Equation of the lineGradient m Point where the line cuts the y axis 2y = 3x x + y – 5 = 0 2x + 3y – 6 = 0 2x + y = 8 y – 3x – 7 = 0 2y + x – 1 = 0 4y = x + 1 2y = 4 – 3x y – x – 2 = 0 Table 3

8. Equation of the lineGradient m Point where the line cuts the y axis 2y = 3x 3/2(0,0) x + y – 5 = 0 (0,5) 2x + 3y – 6 = 0 -2/3(0,2) 2x + y = 8 -2(0,8) y – 3x – 7 = 0 3(0,7) 2y + x – 1 = 0 -1/2(0,0.5) 4y = x + 1 ¼(0,0.25) 2y = 4 – 3x -3/2(0,2) y – x – 2 = 0 1(0,2) Table 3 - solutions

9. Equation of the lineGradient m Point where the line cuts the y axis 3y- x – 6 = 0 2y = x + 2 4y = 4 – 8x 2y – x – 1 = 0 3x + 4y = 12 8y = 5x x + 4y + 10 = 0 y = 5 x – 2y = 0 Table 4

10. Equation of the lineGradient m Point where the line cuts the y axis 3y - x – 6 = 0 1/3(0,2) 2y = x + 2 ½(0,1) 4y = 4 – 8x -2(0,1) 2y – x – 1 = 0 ½(0,0.5) 3x + 4y = 12 -3/4(0,3) 8y = 5x 5/8(0,0) x + 4y + 10 = 0 -1/4(0,-2.5) y = 5 0(0,5) x – 2y = 0 1/2(0,0) Table 4 - solutions

11. Equation of the lineGradient m Point where the line cuts the y axis y – 2x – 5 = 0 y = 4 – 3x x + y + 1 = 0 5y = x + 2 2x + 3y – 6 = 0 x + 2y – 4 = 0 3y = 2x + 1 10x + y = 7 2x + y = 0 Table 5

12. Equation of the lineGradient m Point where the line cuts the y axis y – 2x – 5 = 0 2(0,5) y = 4 – 3x -3(0,4) x + y + 1 = 0 (0,-1) 5y = x + 2 0.2(0,0.4) 2x + 3y – 6 = 0 -2/3(0,2) x + 2y – 4 = 0 -1/2(0,2) 3y = 2x + 1 2/3(0,1/3) 10x + y = 7 -10(0,7) 2x + y = 0 -2(0,0) Table 5 - solutions

13. Equation of the lineGradient m Point where the line cuts the y axis y = 4 4x + 5y – 20 = 0 2y = x + 8 y = 3 - x 4x + 2y – 1 = 0 x + 3y + 12 = 0 2x + 5y – 10 = 0 4x = y x = 5 Table 6

14. Equation of the lineGradient m Point where the line cuts the y axis y = 4 0(0,4) 4x + 5y – 20 = 0 -4/5(0,4) 2y = x + 8 ½(0,4) y = 3 - x (0,3) 4x + 2y – 1 = 0 -2(0,0.5) x + 3y + 12 = 0 -1/3(0,-4) 2x + 5y – 10 = 0 -0.4(0,2) 4x = y 4(0,0) x = 5 undefineddoes not cut y axis Table 6 - solutions