Final answer:
The slope and y-intercept of a linear equation in the form y = a + bx can be identified by the coefficient of x (slope, 'b') and the constant term (y-intercept, 'a'). The correct answer is Option a), where the slope is -2 and the y-intercept is (0, -4).
Step-by-step explanation:
Understanding the slope and y-intercept of a linear equation is crucial in algebra. In the equation y = a + bx, 'b' represents the slope, while 'a' represents the y-intercept. The slope defines the steepness of the line and is constant throughout the line, symbolized as a rise over the run on a graph. The y-intercept is the point where the line crosses the y-axis, represented by the coordinate (0, a).
Using the information provided, if we consider a linear equation in the form y = a + bx, we can determine the slope and y-intercept from the equation itself. The coefficient 'b' is the slope, and the constant term 'a' is the y-intercept. So, if an equation was given as y = -2x - 4, the slope would be -2, and the y-intercept would be (0, -4). This identifies the correct answer as Option a). The slope is -2 and the y-intercept is (0, -4).