Question

Find the slope and the y-intercept of the line. $$y=-2$$

Short answer

The slope of the line \(y = -2\) is 0, and the y-intercept is -2.

Step-by-step solution

Determine the form of the line equation

The first step is to identify the form of the line equation. The given equation is \(y = -2\). In standard form, any straight line can be represented as \(y = mx + c\), where m is the slope, and c is the y-intercept. Our equation doesn't have an x term, which implies that the line is horizontal and does not 'rise' or 'fall' anywhere. That is the characteristic of a line with a slope of 0.

Identify the slope of the line

The 'm' in our standard form of the line equation represents the slope. For our equation \(y = -2\), since there is no x term, the slope m is 0. This is because a horizontal line does not rise or fall, and therefore, its slope is zero. So, the slope of the line \(y = -2\) is 0.

Identify the y-intercept of the line

The 'c' in our standard form of the line equation represents the y-intercept, which is the point where the line crosses the y-axis. For our equation \(y = -2\), since there is no x term, the y-intercept is the constant term, which is -2. Therefore, the y-intercept of the line is at the point (0, -2).