This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here is the solution for Question 1. Question 1 1.1 a) The relationship describes a linear function where the output value (y) is obtained by multiplying the input value (x) by -(1)/(3) and then adding 3. b) To calculate the output values for each input value: • For x = 6: y = -(1)/(3)(6) + 3 = -2 + 3 = 1 • For x = 3: y = -(1)/(3)(3) + 3 = -1 + 3 = 2 • For x = 0: y = -(1)/(3)(0) + 3 = 0 + 3 = 3 • For x = -3: y = -(1)/(3)(-3) + 3 = 1 + 3 = 4 • For x = -6: y = -(1)/(3)(-6) + 3 = 2 + 3 = 5 The output values are 1, 2, 3, 4, 5. c) The completed flow diagram: x Multiply by -(1)/(3) Result Add 3 y The input values are 6, 3, 0, -3, -6. The corresponding output values are 1, 2, 3, 4, 5. d) The table of input and output values: | x | 6 | 3 | 0 | -3 | -6 | |---|---|---|---|----|----| | y | 1 | 2 | 3 | 4 | 5 | e) The x and y values as ordered pairs: (6; 1), (3; 2), (0; 3), (-3; 4), (-6; 5) f) To draw and plot the graph, you would: 1. Draw a Cartesian plane with an x-axis and a y-axis. 2. Plot each of the ordered pairs from part (e) as points on the plane. 3. Draw a straight line connecting these points. This line represents the graph of the function y = -(1)/(3)x + 3. g) The graph is decreasing. This is indicated by the negative coefficient of x (the slope, -(1)/(3)). As the x values increase, the y values decrease. Drop the next question 📸