This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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Here are the solutions to the questions: 3.1.1 I cannot draw graphs directly. To draw the graphs of y = 2x - 4 and y = 2x + 2 on the same set of axes, you can use the following points: For y = 2x - 4: • When x = 0, y = -4. Point: (0, -4) (y-intercept) • When y = 0, 0 = 2x - 4 2x = 4 x = 2. Point: (2, 0) (x-intercept) For y = 2x + 2: • When x = 0, y = 2. Point: (0, 2) (y-intercept) • When y = 0, 0 = 2x + 2 2x = -2 x = -1. Point: (-1, 0) (x-intercept) Plot these points for each line and draw a straight line through them. Label each line with its equation. 3.1.2 Step 1: Identify the y-intercept for y = 2x - 4. The y-intercept occurs when x = 0. y = 2(0) - 4 = -4 Step 2: Identify the y-intercept for y = 2x + 2. The y-intercept occurs when x = 0. y = 2(0) + 2 = 2 The coordinates of the y-intercepts are: For y = 2x - 4: (0, -4) For y = 2x + 2: (0, 2) 3.1.3 Step 1: Calculate the x-intercept for y = 2x - 4. The x-intercept occurs when y = 0. 0 = 2x - 4 4 = 2x x = 2 Step 2: Calculate the x-intercept for y = 2x + 2. The x-intercept occurs when y = 0. 0 = 2x + 2 -2 = 2x x = -1 The coordinates of the x-intercepts are: For y = 2x - 4: (2, 0) For y = 2x + 2: (-1, 0) 3.1.4 Both graphs are linear. Explanation: Both equations are in the form y = mx + c, where m and c are constants. This is the standard form for a linear equation, meaning the highest power of the variable x is 1. 3.1.5 The graph of y = 2x - 4 is increasing. Explanation: The slope (m) of the line y = 2x - 4 is 2. Since the slope is positive (m > 0), the graph is increasing. 3.2.1 Step 1: Substitute x = 0 into the equation y = 2x - 4. y = 2(0) - 4 Step 2: Simplify the expression. y = 0 - 4 y = -4 3.2.2 Step 1: Substitute y = 0 into the equation y = 2x - 4. 0 = 2x - 4 Step 2: Solve for x. 4 = 2x x = (4)/(2) x = 2 3.2.3 Step 1: Set the two equations equal to each other to find the point of intersection. The equations are y = 2x - 4 and y = 2x + 2. 2x - 4 = 2x + 2 Step 2: Solve for x. Subtract 2x from both sides: -4 = 2 Step 3: Interpret the result. The statement -4 = 2 is false. This means there is no value of x for which the two equations are equal. Therefore, the lines are parallel and do not intersect. The point of intersection is No intersection (lines are parallel). Send me the next one 📸