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
a) To complete Table 2, substitute each value of x into the relation y = -2x + 3. Step 1: Calculate y for each x value. For x = -2: y = -2(-2) + 3 = 4 + 3 = 7 For x = -1: y = -2(-1) + 3 = 2 + 3 = 5 For x = 0: y = -2(0) + 3 = 0 + 3 = 3 For x = 2: y = -2(2) + 3 = -4 + 3 = -1 For x = 3: y = -2(3) + 3 = -6 + 3 = -3 For x = 4: y = -2(4) + 3 = -8 + 3 = -5 Step 2: Complete the table with the calculated values. |c|c|c|c|c|c|c|c|c|c| x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ y & 9 & 7 & 5 & 3 & 1 & -1 & -3 & -5 & -7 \\ b) To draw the graph of the equation y = -2x + 3, plot the points from the completed table: (-3, 9), (-2, 7), (-1, 5), (0, 3), (1, 1), (2, -1), (3, -3), (4, -5), (5, -7). Use the given scale: 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis. Connect the points with a straight line. (As an AI, I cannot draw the graph for you, but these are the points you would plot.) c) From the graph, determine the value of: i) the slope; The equation is y = -2x + 3, which is in the form y = mx + c, where m is the slope. Step 1: Identify the slope from the equation. The coefficient of x is the slope. The slope is -2. ii) x when y = -5. Step 1: Substitute y = -5 into the equation y = -2x + 3. -5 = -2x + 3 Step 2: Solve for x. -5 - 3 = -2x -8 = -2x x = (-8)/(-2) x = 4 Send me the next one 📸