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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Okay, Akabongwe, let's continue with the next section of your work. Task 2.2: Classification (2 Marks) Step 1: Classify the equations. The equations y = (1)/(2)x + 2, y = 2x - 4, and y = -2x + 2 are all in the form y = mx + c. This is the standard form for a linear equation. Step 2: Justify the classification. When graphed, equations of the form y = mx + c always produce straight lines. Answer: The equations are linear because their graphs are straight lines. Phase 3: Investigating Intercepts (12 Marks) Task 3.1: Visual Identification (6 Marks) Step 1: Calculate the y-intercept (set x=0) and x-intercept (set y=0) for each equation. Equation 1: y = (1)/(2)x + 2 y-intercept (x=0): y = (1)/(2)(0) + 2 = 2. Ordered pair: (0; 2). x-intercept (y=0): 0 = (1)/(2)x + 2 -2 = (1)/(2)x x = -4. Ordered pair: (-4; 0). Equation 2: y = 2x - 4 y-intercept (x=0): y = 2(0) - 4 = -4. Ordered pair: (0; -4). x-intercept (y=0): 0 = 2x - 4 4 = 2x x = 2. Ordered pair: (2; 0). Equation 3: y = -2x + 2 y-intercept (x=0): y = -2(0) + 2 = 2. Ordered pair: (0; 2). x-intercept (y=0): 0 = -2x + 2 2x = 2 x = 1. Ordered pair: (1; 0). Step 2: Complete the table. |c|c|c| Equation & y-intercept (Ordered Pair) & x-intercept (Ordered Pair) \\ Eq 1: y = (1)/(2)x + 2 & (0; 2) & (-4; 0) \\ Eq 2: y = 2x - 4 & (0; -4) & (2; 0) \\ Eq 3: y = -2x + 2 & (0; 2) & (1; 0) \\ Task 3.2: Algebraic Verification (Equation 2) (4 Marks) Workspace for Equation 2 (y = 2x - 4): Step 1: Calculate the value of y when x = 0. y &= 2x - 4 \\ y &= 2(0) - 4 \\ y &= 0 - 4 \\ y &= -4 The y-intercept is (0; -4). Step 2: Solve for the value of x when y = 0. y &= 2x - 4 \\ 0 &= 2x - 4 \\ 4 &= 2x \\ x &= (4)/(2) \\ x &= 2 The x-intercept is (2; 0). Task 3.3: Synthesis of Intercepts (2 Marks) Step 1: Define the y-intercept. The y-intercept is the point where the graph crosses the y-axis. At this point, the x-coordinate is always zero. Step 2: Relate the y-intercept to the equation. For a linear equation in the form y = mx + c, the y-intercept is the point (0, c), where c is the constant term. Answer: The y-intercept is the point where the graph intersects the y-axis. Its x-coordinate is always 0, and its y-coordinate is the value of the function when x=0. In the equation y = mx + c, the y-intercept is (0, c). 3 done, 2 left today. You're making progress.