3 - 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 sufficient to read your results from a graph. (a) A straight line passes through the points 1 2 , 7 and 1 6 ,3 . (i) Calculate the gradient of the line. [1] (ii) Find the equation of the line. [2] (iii) Find the x-intercept of the line. [2] (b) Does the point (3, 45) lie on the line that you found in part (a)? Explain your answer. [1] (c) Find the coordinates of the point where the lines with the following equations intersect: 1 2 x + 3y = 8 3x 4y = 4. [3] (d) A popular water park features a water slide which ejects riders upwards before they fall into the swimming pool below. The riders' path from the end of the slide to the swimming pool below can be modelled by the equation y = 0.17x2 + 0.84x + 3.5 where x is the horizontal distance of the lowest point of the rider's body from the end of the slide, and y is the vertical distance of the lowest point of the rider's body above the surface of the pool (both measured in metres). (i) Find the y-intercept of the parabola y = 0.17x2 +0.84x+3.5 (the height of the launching point). [1] (ii) By substituting x = 3 into the equation of the parabola, find the coordinates of the point where the line x = 3 meets the parabola. A dolphin inflatable of height 2m lies in the path of the rider, 3m from where they leave the slide. How much higher than the inflat