Find the equation of a line parallel to 2y = 3(x - 2) and passing through the point (2, 3).

Here are the solutions to the problems. Question 19: The diagram for this question is not visible in the provided image. Therefore, it is not possible to find the value of x. --- Question 20: Given: A line parallel to 2y = 3(x - 2) and passing through the point (2, 3). To find: The equation of this line. Step 1: Find the slope of the given line. First, rewrite the given equation in slope-intercept form (y = mx + c). 2y = 3(x - 2) 2y = 3x - 6 Divide by 2: y = (3)/(2)x - 3 The slope of this line is m_1 = (3)/(2). Step 2: Determine the slope of the new line. Since the new line is parallel to the given line, their slopes are equal. So, the slope of the new line is m_2 = (3)/(2). Step 3: Use the point-slope form to find the equation of the new line. The new line passes through (x_1, y_1) = (2, 3) and has a slope m = (3)/(2). The point-slope form is y - y_1 = m(x - x_1). y - 3 = (3)/(2)(x - 2) Step 4: Convert the equation to slope-intercept form. y - 3 = (3)/(2)x - (3)/(2) × 2 y - 3 = (3)/(2)x - 3 Add 3 to both sides: y = (3)/(2)x - 3 + 3 y = (3)/(2)x Step 5: Compare with the given options. The calculated equation matches option C. The final answer is C. y = (3)/(2)x. --- Question 21: Given: The expression (5x+3)/(6x(x+1)). To find: The values of x for which the expression is undefined. Step 1: Identify the condition for an expression to be undefined. A rational expression is undefined when its denominator is equal to zero. Step 2: Set the denominator to zero and solve for x. The denominator is 6x(x+1). 6x(x+1) = 0 For this product to be zero, at least one of the factors must be zero. Case 1: Set the first factor to zero. 6x = 0 x = (0)/(6) x = 0 Case 2: Set the second factor to zero. x+1 = 0 x = -1 Step 3: List the values of x. The expression is undefined when x = 0 or x = -1. The set of values is \0, -1\. Step 4: Compare with the given options. The calculated set matches option B. The final answer is B. \0, -1\. --- Question 22: Given: A man is five times as old as his son. In four years time, the product of their ages would be 340. The son's current age is y. To find: Express the product of their ages in terms of y. Step 1: Define current ages in terms of y. Son's current age = y Man's current age = 5y Step 2: Define ages in four years time. Son's age in four years = y + 4 Man's age in four years = 5y + 4 Step 3: Express the product of their ages in four years in terms of y. Product of their ages in four years = (y + 4)(5y + 4) Step 4: Expand the expression. (y + 4)(5y + 4) = y(5y) + y(4) + 4(5y) + 4(4) = 5y^2 + 4y + 20y + 16 = 5y^2 + 24y + 16 The product of their ages in terms of y is 5y^2 + 24y + 16. This expression is equal to 340 according to the problem statement. The final answer is 5y^2 + 24y + 16.