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.
ScanSolve AI Answer
Let's solve question 4. The relation is given by y = 7x + c. a) Step 1: Use one of the complete (x, y) pairs from the table to find the value of c. Let's use the pair (1, 2). Substitute x=1 and y=2 into the equation y = 7x + c. 2 = 7(1) + c 2 = 7 + c Step 2: Solve for c. c = 2 - 7 c = -5 b) Now that we know c = -5, the relation is y = 7x - 5. We will use this to complete the table. Step 1: Calculate y for x = -1. y = 7(-1) - 5 = -7 - 5 = -12 Step 2: Calculate y for x = 0. y = 7(0) - 5 = 0 - 5 = -5 Step 3: Calculate y for x = 2. y = 7(2) - 5 = 14 - 5 = 9 Step 4: Calculate y for x = 3. y = 7(3) - 5 = 21 - 5 = 16 Step 5: Calculate y for x = 4. y = 7(4) - 5 = 28 - 5 = 23 The completed table is: x: -2, -1, 0, 1, 2, 3, 4, 5 y: -19, -12, -5, 2, 9, 16, 23, 30 c) (i) This step requires drawing axes. As an AI, I cannot physically draw. You need to: • Draw two perpendicular lines on your graph sheet. • Label the horizontal axis OX (x-axis) and the vertical axis OY (y-axis). • Use a scale of 2 cm to represent 1 unit on the x-axis. • Use a scale of 2 cm to represent 5 units on the y-axis. c) (ii) This step requires marking the axes. As an AI, I cannot physically mark axes. You need to: • Mark the x-axis from -5 to 5. • Mark the y-axis from -25 to 35. d) This step requires plotting points and drawing a line. As an AI, I cannot physically perform this action. You need to: • Plot the ordered pairs (x, y) from the completed table in part (b) on your graph sheet. The points are: (-2, -19), (-1, -12), (0, -5), (1, 2), (2, 9), (3, 16), (4, 23), (5, 30). • Join these plotted points with a straight line using a ruler. e) Step 1: To find the value of y when x = 3.2 using the graph, you would locate x = 3.2 on the x-axis, move vertically to the line you drew, and then move horizontally to the y-axis to read the corresponding y value. Using the equation y = 7x - 5 for an exact calculation: y = 7(3.2) - 5 y = 22.4 - 5 y = 17.4 5 done, 0 left today. You're making progress.