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
Okay, Akabongwe, let's get this graph constructed! Equation 3: y = -2x + 2 Step 1: Calculate output (y) values for Equation 3. • For x = -2: y = -2(-2) + 2 = 4 + 2 = 6 • For x = -1: y = -2(-1) + 2 = 2 + 2 = 4 • For x = 0: y = -2(0) + 2 = 0 + 2 = 2 • For x = 0.5: y = -2(0.5) + 2 = -1 + 2 = 1 • For x = 2: y = -2(2) + 2 = -4 + 2 = -2 Step 2: Complete the table for Equation 3. |c|c|c|c|c|c| Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ Output (y) & 6 & 4 & 2 & 1 & -2 \\ Ordered Pair (x; y) & (-2; 6) & (-1; 4) & (0; 2) & (0.5; 1) & (2; -2) \\ Task 2.1: Graph Construction Step 3: Draw the Cartesian plane. • On your graph paper, draw a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). • Label the x-axis from -5 to 5 and the y-axis from -5 to 5, marking integer values clearly. Step 4: Plot the ordered pairs for all three equations. • For Equation 1 (y = (1)/(2)x + 2): Plot (-2; 1), (-1; 1.5), (0; 2), (0.5; 2.25), (2; 3). All these points are within the specified range. • For Equation 2 (y = 2x - 4): Plot (0; -4), (0.5; -3), (2; 0). Note that (-2; -8) and (-1; -6) fall outside the y-axis range of -5 to 5, so they cannot be plotted on this specific graph. • For Equation 3 (y = -2x + 2): Plot (-1; 4), (0; 2), (0.5; 1), (2; -2). Note that (-2; 6) falls outside the y-axis range of -5 to 5, so it cannot be plotted on this specific graph. Step 5: Draw and label the lines. • Using a ruler, draw a solid line through the plotted points for Equation 1. Label this line "Equation 1". • Using a ruler, draw a solid line through the plotted points for Equation 2. Use a different color or line style (e.g., dashed) for this line. Label it "Equation 2". • Using a ruler, draw a solid line through the plotted points for Equation 3. Use a third different color or line style (e.g., dotted) for this line. Label it "Equation 3". That's 2 down. 3 left today — send the next one.