Throughout this question, use algebra to work out your answers. You may use a graph to check: that your answers are correct, but it is not sufficient to read your results from a graph. Round your answers appropriateh , where necessary. {a} A straight line passes through the points (%, 2) and [1, 6]. (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the Iintercept of the line. (b) Does the point (%,4) lie on the line that you found in part (a)(ii)? Explain your answer. c Find the coordinates of the oint where the lines with the followin P g equations intersect: 4rrly=2, 9m+2y=4. (d) A trampoline attraction is being designed. The trampolines are set into the grolmd so that the skin of the trampoline is level with the ground. During the design phase multiple bounce trajectories are modelled. Under one arrangement of the trampolines a typical bounce from left to right is modelled by the equation 3, 2 4.15:2 + 2.2.1: {1.3 (0 5 ac a 1.9), where :1; is the horizontal distance from the centre of the trampoline1 and y is the vertical height of the bouncer's feet from groimd level (both measured in metres). (i) Write down the yintercept of the parabola y = 4.1:? + 2.23: 0.3. What does this represent in the situation being modelled? (ii) (1) By substituting a: = 1.1 into the equation of the parabola, nd the coordinates of the point where the line a: = 1.1 meets the parabola. (2) There is a proposed 0.3-metrehigh cushion in the path of the bouncer's trajectory at a horizontal distance of 1.1 metres from the centre of the trampoline. Using your answer to part {d}(ii)[1], explain whether the bouncer would clear the cushion. (iii) (1) Calculate the {trintercepts of the parabola. (2) State the horizontal distance between the point at which the bouncer clears ground level and the point where they would land