I have the following question to answer which involves various algebra etc. and I have always struggled with this area. Could someone help please ad I need to use algebra to work out all answers:

(a) A straight line passes through the points (2,8) and (4,4). (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 (5.5,6.5) lie on the line that you found in part (a)(ii)? Explain your answer. [2]

(c) Find the coordinates of the point where the lines with the following equations intersect: 2x6y = 9, 3x + 7y = 3 2. [3]

(d) A mini-golf course is planned. Looking at the course from above, one section of the course has a straight wall on the left-hand side leading up to a small ledge, shaped like a parabola, which can be modelled by the equation y = 0.5x2 + 1.5x + 2.0, where x is the horizontal distance of the parabolic ledge from the left-hand wall, and y is the distance of the parabolic ledge from the start line of the section (both measured in metres). Figure below shows a bird's-eye view of the section of the course:

\f\f\f