Final answer:
The equation of the straight line passing through the points (3,2) and intersecting the x-axis and y-axis at points A and B respectively, where OA - OB = 2, is y = 2x - 4.
Step-by-step explanation:
To find the equation of the straight lines passing through the points (3,2) and intersecting the x-axis and y-axis at points A and B respectively, we need to determine the coordinates of A and B and then find the slope of the line.
Let A have coordinates (a,0) and B have coordinates (0,b). Since OA - OB = 2, we have a - 0 = 2, which implies a = 2.
Hence, point A is (2, 0). Similarly, we have 0 - b = 2, which implies b = -2. Hence, point B is (0, -2).
Using the two coordinates, (3,2) and (2,0), we can plug them into the slope-intercept form of a line equation, y = mx + b, where m is the slope.
By calculating the slope, which is (2 - 0)/(3 - 2) = 2, and substituting the coordinates into the equation, we get y = 2x - 4 as the equation of the straight line passing through the given points.