How do you write the equation of a line with slope 3 and y-intercept 2?

The equation of the line is \( y = 3x + 2 \).

To write the equation of a line, you need to know the slope (gradient) and the y-intercept. The slope is a measure of how steep the line is, and the y-intercept is the point where the line crosses the y-axis. The general form of the equation of a line in slope-intercept form is \( y = mx + c \), where \( m \) represents the slope and \( c \) represents the y-intercept.

In this case, the slope \( m \) is given as 3, and the y-intercept \( c \) is given as 2. Plugging these values into the slope-intercept form, we get:

\[ y = 3x + 2 \]

This equation tells us that for every unit increase in \( x \), the value of \( y \) increases by 3 units, and when \( x \) is 0, \( y \) is 2. This is a straightforward way to represent a linear relationship between \( x \) and \( y \).

If you were to graph this equation, you would start at the point (0, 2) on the y-axis. From there, you would move up 3 units for every 1 unit you move to the right, creating a straight line. This visual representation helps to understand how the slope and y-intercept define the line's position and angle on the graph.