Hi Tutor,Can you help me out with question 3 please. Thank you.

Question 3 i 20 marks Throughout this question, you should use algebra to work out your answers. You may use a graph to check that your answers are correct, but it is not su'lctent to read your results from a graph. 3 1 (a) A straight line passes through the points (1, i) and (76, '2). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the :tintercept of the line. (1)) Does the point (3, 1) lie on 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 6 +7 :1 1 3 _, :7. (d) A fountain is planned for a city centre. The fountain features arcs of water which pass over a footpath. The water arcs are being modelled on a computer to get the settings for the fountain right. One setting of the fountain spout creates an arc of water that can be modelled by the equation y: 41.3322 . 1.533 . 0.8, where a: is the horizontal distance of the water arc from the spout of the fountain, and y is the vertical distance of the water arc above the ground (both measured in metres). (i) Find the yintercept of the parabola y 7 e033? l 1.53: l 0.8. What does the yintercept represent in the physical situation being modelled? (ii) i. Find the coordinates of the point where the line a: = 4 meets the parabola. ii. Using your answer to part (d)(ii) i, explain whether the water would go higher than a sculpture of height 1.4m that stands 4m from the spout of the fountain and lies in the path of the water. (iii) i. Find the rintercepts of the parabola. Give your answers in decimal form, correct to two decimal places. ii. Assume that the water lands on the ground. Use your answers from part (d)(i) and part (d) (iii) i to nd the horizontal distance between the spout of the fountain, and where the water rst lands. (iv) Find the maximum height reached by the water. [1] [2] [2] [3] [3]