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
Here's the solution for Exercise 6.6, Question 1: The equation given is 2x + y - 1 = 0. Step 1: Rearrange the equation to solve for y. y = -2x + 1 Step 2: Create a table of values by choosing several x-values and calculating the corresponding y-values. | x | y = -2x + 1 | (x, y) | |-----|---------------|----------| | -1 | y = -2(-1) + 1 = 2 + 1 = 3 | (-1, 3) | | 0 | y = -2(0) + 1 = 0 + 1 = 1 | (0, 1) | | 1 | y = -2(1) + 1 = -2 + 1 = -1 | (1, -1) | | 2 | y = -2(2) + 1 = -4 + 1 = -3 | (2, -3) | Step 3: Determine the x-intercept. The x-intercept is the point where the graph crosses the x-axis, meaning y = 0. 0 = -2x + 1 2x = 1 x = (1)/(2) The x-intercept is ((1)/(2), 0). Step 4: Determine the y-intercept. The y-intercept is the point where the graph crosses the y-axis, meaning x = 0. y = -2(0) + 1 y = 1 The y-intercept is (0, 1). To draw the graph, plot the points from the table of values, including the x-intercept and y-intercept, and then draw a straight line through them.