(a) A straight line passes through the points (in E] and (g, 2). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the .rintercept of the line. (b) Does the line 3,: = %.7: + 3 intersect with the line that you found in part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: 1 9 =4 '1" 2y I 3 3.1'+ y=12. (d) Using a throwing stick, Dorninic can throw his dog's ball across the park. Assume that the park is at. The path of the hall can be modelled by the equation y = 4.0232 +z+ 2.5. where r is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres). (i) Find the yintercept of the parabola y = 41.0212 + r + 2.6 (the point at which the hall leaves the throwing stick). (ii) (1) By substituting .r = 15 into the equation of the parabola, nd the coordinates of the point where the line .1- = 15 meets the parabola. (2) Using your answer to part (d}(ii){1), explain whether the ball goes higher than a tree of height 4m that stands 15m from Dorninic and lies in the path of the ball. (iii) (1) Find the .rintercepts of the parabola. Give your answers in decimal form, correct to two decimal places. (2) Assume that the ball lands on the ground. Use your answer from part (d)(iii)(1) to nd the horizontal distance between where Dominic throws the hall, and where the ball rst lands. (iv) Find the maximum height reached by the ball