Final answer:
The domain and range for a linear equation like y = a + bx are usually all real numbers unless there's a specific limitation. An x-intercept occurs when y=0 and a y-intercept occurs when x=0; 'a' represents the y-intercept and 'b' is the slope.
Step-by-step explanation:
When evaluating a linear equation such as y = a + bx, it is essential to understand its domain, range, x-intercept, and y-intercept. The domain is all the possible x-values that a function can accept, while the range consists of all possible y-values that a function can output. An x-intercept is the point where the function crosses the x-axis, which implies that y=0. Similarly, a y-intercept is where the function crosses the y-axis, indicating x=0.
For the equation y = a + bx, the domain would typically be all real numbers unless there's a specific restriction. Considering that 'b' represents the slope and 'a' is the y-intercept, if both 'a' and 'b' are real numbers, the function's range is also all real numbers. However, if there's a condition that limits the function, such as it only takes positive numbers, then the domain and/or range would be restricted accordingly. To determine the x-intercept, set y=0 and solve the equation for x. For the y-intercept, set x=0 and solve for y, which is simply 'a'. Thus, using the function y = a + bx, if b and a are not zero, then normally there would be different x and y-intercepts; however, if 'a' is zero, the function would pass through the origin, and both intercepts would be (0,0).