The slope of the line represented by the equation y = 3 is undefined.
To explain this further, a slope describes how steep a line is and is calculated using the formula m = (y2 – y1) / (x2 – x1). In the case of the line y = 3, the value of y is constant at 3, regardless of the value of x. This means that as you move along the line, there is no change in the vertical direction (change in y), while the horizontal direction (change in x) can vary.
Let’s consider two points on the line: (0, 3) and (3, 3). If we calculate the slope using the slope formula:
m = (3 - 3) / (3 - 0) = 0 / 3 = 0
This indicates that the line is horizontal. However, if we think about a vertical line instead, the slope would be a situation where x remains constant, and we only change y. Since we cannot divide by zero, the slope of such lines is classified as undefined.
Thus, the horizontal line y = 3 has a slope of 0, not undefined. If we mistakenly interpret a constant function in a different context, it’s crucial to grasp that here, our slope remains defined as 0 when considering horizontal movement.