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
1.1 Sketch the graph of (x)/(2) + (y)/(3) = 1 Step 1: Identify the intercepts. The equation is in the intercept form (x)/(a) + (y)/(b) = 1, where a is the x-intercept and b is the y-intercept. From the given equation, a = 2 and b = 3. So, the x-intercept is (2, 0) and the y-intercept is (0, 3). Step 2: Describe the sketch. To sketch the graph, plot the x-intercept at (2, 0) on the x-axis and the y-intercept at (0, 3) on the y-axis. Then, draw a straight line connecting these two points. The graph is a straight line passing through (2, 0) and (0, 3). 1.2 Is the graph in Q1.1 a function or a relation? Step 1: Analyze the equation. The equation (x)/(2) + (y)/(3) = 1 can be rewritten to solve for y: (y)/(3) = 1 - (x)/(2) y = 3 (1 - (x)/(2)) y = 3 - (3)/(2)x This is a linear equation in the form y = mx + c. Step 2: Determine if it's a function or relation. For every input value of x, there is exactly one output value of y. This means the graph passes the vertical line test. Therefore, the graph is a function. 1.3 Is the graph in Q1.1 continuous? Step 1: Consider the nature of the graph. The graph of (x)/(2) + (y)/(3) = 1 is a straight line. Step 2: Determine continuity. A straight line can be drawn without lifting the pen, meaning there are no breaks, jumps, or holes in the graph. Therefore, the graph is continuous. Drop the next question!