How do you write the equation of a line with slope 1/2 and y-intercept -2?

The equation of the line is \( y = \frac{1}{2}x - 2 \).

To write the equation of a line, you need to know the slope (gradient) and the y-intercept. The general form of the equation of a line is \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. In this case, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( c \) is -2.

The slope tells you how steep the line is. A slope of \( \frac{1}{2} \) means that for every 2 units you move horizontally to the right, the line moves 1 unit up. The y-intercept is the point where the line crosses the y-axis. Here, the line crosses the y-axis at -2.

So, substituting the given slope and y-intercept into the general form, you get \( y = \frac{1}{2}x - 2 \). This equation tells you that for any value of \( x \), you can find the corresponding value of \( y \) by multiplying \( x \) by \( \frac{1}{2} \) and then subtracting 2. For example, if \( x = 4 \), then \( y = \frac{1}{2} \times 4 - 2 = 2 - 2 = 0 \).

This equation is useful for graphing the line or finding specific points on the line. Remember, the slope and y-intercept are key components in understanding the behaviour of the line.