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
To find the value of a, we need to use the property that parallel lines have the same slope. Step 1: Calculate the slope of the line passing through the points (3, 0) and (0, 2). The formula for the slope m between two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (3, 0) and (x_2, y_2) = (0, 2). m_1 = (2 - 0)/(0 - 3) = (2)/(-3) = -(2)/(3) Step 2: Identify the slope of the second straight line. The equation of the second line is given as y = ax - 3. This equation is in the slope-intercept form y = mx + c, where m is the slope. So, the slope of the second line is m_2 = a. Step 3: Equate the slopes since the lines are parallel. Since the two lines are parallel, their slopes must be equal: m_1 = m_2. a = -(2)/(3) Comparing this result with the given options, the correct answer is -(2)/(3). The final answer is -(2)/(3). Last free one today — make it count tomorrow, or type /upgrade for unlimited.