Final answer:
The 'a' and 'b' in the equation X/a + Y/b = 1 are constants that determine the y-intercept and slope of the line it represents. Rearranging it in the form Y = b - (b/a)X helps to find specific Y values by substituting X.
Step-by-step explanation:
The equation X/a + Y/b = 1 represents a linear equation in two variables, X and Y, where 'a' and 'b' are constants that give the equation its specific properties. For instance, if you rearrange the equation to solve for Y, it can be expressed as Y = b - (b/a)X. Here, b is the y-intercept of the line, which is the point where the line crosses the Y-axis, and -b/a is the slope of the line, which indicates the steepness and direction of the line. A positive slope means the line goes upward to the right, a negative slope means it goes downward to the right, and a slope of zero indicates a horizontal line.
To find a specific solution for Y, you would substitute a value for X, the independent variable, and calculate the corresponding value of Y, the dependent variable. For example, if a = 2 and b = 4 and you choose X = 2, the equation would be simplified to 1 + Y/4 = 1, which, when solved, gives Y = 0.