Final answer:
The line represented by y = 3 has a slope of 0, indicating a horizontal line. The line represented by x = 3 has an undefined slope, which characterizes a vertical line. The slope is a key concept in the algebra of straight lines.
Step-by-step explanation:
The slope of the line y = 3 is 0 because it is a horizontal line. In the equation y = mx + b, the slope is represented by m, and in this case, it does not change as x changes. There is no 'rise' in the vertical direction when you move along the line, so the slope is 0.
The slope of the line x = 3 is undefined because it is a vertical line. Vertical lines do not have a slope since you cannot form a ratio of rise over run, as the 'run' (change in x) would be 0, and division by zero is undefined in mathematics.
This concept of slope is crucial for understanding the shape of a line, as it represents the 'steepness'. The slope along with the y-intercept determines the shape of a line in the Cartesian coordinate system. Remember, y = mx + b is the formula for a straight line where m is the slope and b is the y-intercept.