What is the equation of a line in slope-intercept form with a slope of 3 and a y-intercept of -2?

The equation of a line in slope-intercept form is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is given as 3, which means that for every unit increase in the x-value, the y-value increases by 3. The y-intercept is given as -2, indicating that the line crosses the y-axis at the point (0, -2).

When substituting the given values into the slope-intercept formula, you replace m with 3 and b with -2. This results in the equation y = 3x - 2.

This correctly reflects both the slope and the y-intercept as specified in the question. The position of -2 as the y-intercept ensures that when x is 0, y is indeed -2, aligning with the definition of the y-intercept.

Understanding this format and the relationship between the slope, the y-intercept, and the resulting linear equation is crucial for solving similar problems in mathematics.