Student’s Name Professor’s Name Mathematics Date of submission 56705540259000Question 1 – 10 marks This question is based on your work on MU123 up to and including Unit 6. (a) (i) Find the gradient of the straight line that passes through the points (3, −4) and (−3, 5). Gradient=5-(-4)-3-3 =9/-6=3/-2 The gradient will be -3/2 (ii) Use this gradient to find the equation of the line, clearly showing each step of your method. Equation of a straight line is given by y=mx+c y and x are the y and x-intercepts respectively c is constant Where m is the gradient, Y=3/-2x+c (b) Use the equation that you found in part (a) to determine whether or not the point (−1, 2) lies on this line. Y=3/-2x+c 2=3/-2(-1) +c C=2-(3/2) C=(1/2) The point lies on the line (c) (i) Use algebra to find the x-intercept of the line that you found in part (a), clearly showing each step of your method. Y=3/-2x+1/2 At intercept y=0 0=-3/-2x+1/2 3/2x=1/2 X=1/3 (1/3,0) (ii) What is the y-intercept? 2y=-3x+1 At y intercept x=0 Hence 2y=1 Y=1/2 (0, 1/2) (d) Plot the two points given in part (a), and draw a line through them. Use this plot to check that your answers to parts (a), (b) and (c) are sensible.

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