How do you find the equation of a line parallel to y = 3x + 2?

To find the equation of a line parallel to \( y = 3x + 2 \), use the same gradient, 3.

A line parallel to another will have the same gradient (or slope). In the equation \( y = 3x + 2 \), the gradient is the coefficient of \( x \), which is 3. Therefore, any line parallel to this one will also have a gradient of 3.

To write the equation of a parallel line, you need to use the form \( y = mx + c \), where \( m \) is the gradient and \( c \) is the y-intercept. Since the gradient \( m \) must be 3 for the lines to be parallel, the equation will look like \( y = 3x + c \), where \( c \) can be any number.

For example, if you want a specific parallel line that passes through a particular point, say (1, 4), you can substitute this point into the equation to find \( c \). Using the point (1, 4):

\[ 4 = 3(1) + c \]

\[ 4 = 3 + c \]

\[ c = 1 \]

So, the equation of the line parallel to \( y = 3x + 2 \) that passes through the point (1, 4) is \( y = 3x + 1 \).

In summary, to find the equation of a line parallel to \( y = 3x + 2 \), keep the gradient the same (3) and adjust the y-intercept \( c \) as needed based on any specific points the line must pass through.