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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Please note: The equation relating x and y for Question 1 is not provided in the image. For the purpose of demonstrating the solution, I will assume the linear function y = x + 1. If the actual function is different, the calculated values and subsequent answers will change. QUESTION 1 Step 1: Calculate the missing values in the table using the assumed function y = x + 1. For x = -2: y = -2 + 1 = -1 For x = -1: y = -1 + 1 = 0 For x = 0: y = 0 + 1 = 1 For x = 1: y = 1 + 1 = 2 For x = 2: y = 2 + 1 = 3 The completed table of values is: |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -1 & 0 & 1 & 2 & 3 \\ Step 2: Plot the points on graph paper. The points to plot are: (-2, -1), (-1, 0), (0, 1), (1, 2), (2, 3). Step 3: Draw the graph. When plotted, these points form a straight line. Step 4: State whether the graph is linear or non-linear. Based on the assumed function y = x + 1, the graph is linear. Step 5: Determine the gradient of the graph. Using two points from the table, for example, (0, 1) and (1, 2): m = (y_2 - y_1)/(x_2 - x_1) = (2 - 1)/(1 - 0) = (1)/(1) = 1 The gradient of the graph is 1. Step 6: Determine the y-intercept. The y-intercept is the value of y when x = 0. From the table, when x=0, y=1. The y-intercept is 1. Step 7: Determine the x-intercept. The x-intercept is the value of x when y = 0. Using the assumed function y = x + 1: 0 = x + 1 x = -1 The x-intercept is -1. QUESTION 2 The question asks to find two integers, r and s, whose product is c and whose sum is b for a trinomial in the form x^2 + bx + c. This describes the general method for factoring a quadratic trinomial of the form x^2 + bx + c. To factor it into (x+r)(x+s), you need to find two integers, r and s, such that: Their product r × s is equal to the constant term c. Their sum r + s is equal to the coefficient of the x term, b. Since no specific trinomial (i.e., no specific values for b and c) is provided in the question, specific integers r and s cannot be determined. Send me the next one 📸