Throughout this question, you should use algebra to work out your answers, shout-Eng your working cleariy. You may use a graph to check that your answers are correct, but it is not sufficient to reaol your results from a graph. in} lb) {cl (*1) A straight line passes through the points (3. 'Er) and (3, 121-). {i} Calculate the gradient of the line. [ii] Find the equation of the line. [iii] Find the m-intercept of the line. Does the line y = 51 + 3 intersect with the line that you found in part {a}? Explain your answer. Find the coordinates of the point where the lines with the following equations intersect: 4e+3y= 32. 2s+y=. Using a throwing stick, Dominic can throw his dog's ball across the park. Assume that the park is at. The path of the ball can be modelled by the equation y = .2x2 +x+ 1a. 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 y-intercept of the parabola y = [l.[12x2 + a + 1.8 [the point at which the ball leaves the throwing stick}. [ii] [1} By substituting at = 2E] into the equation of the parabola1 nd the coordinates of the point where the line a = 2U meets the parabola. {2} Using your answer to part {d}[ii)[l}, explain whether the ball gem higher than a tree of height 3.5m that stands 20m from Dominic and lies in the path of the ball. [iii] [1] Find the ar-intercepts 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 thrcsvs the ball, and where the ball rst lands. {iv} Find the maximum height reached by the ball