How do you write the equation of a line parallel to y = 4x + 2?

To write the equation of a line parallel to \( y = 4x + 2 \), use the same gradient, 4.

In more detail, the equation of a line in the form \( y = mx + c \) represents a straight line where \( m \) is the gradient (or slope) and \( c \) is the y-intercept. For two lines to be parallel, they must have the same gradient. The given line \( y = 4x + 2 \) has a gradient of 4.

To write the equation of a line parallel to this one, you need to keep the gradient the same, which is 4. The general form of the equation for any line parallel to \( y = 4x + 2 \) will be \( y = 4x + c \), where \( c \) can be any constant. This constant \( c \) represents the y-intercept of the new line, which can be different from the original line's y-intercept.

For example, if you want a line parallel to \( y = 4x + 2 \) that passes through the point (1, 3), you would substitute \( x = 1 \) and \( y = 3 \) into the equation \( y = 4x + c \) to find \( c \):

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

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