What is the slope-intercept form of the equation for a line with a slope of 3 and a y-intercept of -1?

To derive the slope-intercept form of a line's equation, you need to utilize the formula (y = mx + b), where (m) represents the slope of the line and (b) signifies the y-intercept.

In this case, you are given a slope of 3 and a y-intercept of -1. Substituting these values into the formula, you replace (m) with 3 and (b) with -1. This results in the equation:

[y = 3x - 1]

This formulation confirms that for every increase of 1 unit in (x), (y) increases by 3 units, hence capturing the slope accurately. Additionally, it indicates that the line crosses the y-axis at -1, aligning with the given y-intercept.

These specific values distinctly lead to the final equation, ensuring that the slope and y-intercept match the conditions of the problem accurately.