Which equation fits a line that is parallel to the line y = 2x + 4?

1 answer

To find a line that is parallel to the line given by the equation \( y = 2x + 4 \), we need to recognize that parallel lines have the same slope.

In the equation \( y = 2x + 4 \), the slope is 2. Therefore, any line that is parallel to this line will also have a slope of 2.

The general form of the equation of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

So, a line that is parallel to \( y = 2x + 4 \) can be expressed as:

\[ y = 2x + b \]

where \( b \) can be any real number. For example:

  • If \( b = 0 \), the equation is \( y = 2x \).
  • If \( b = 1 \), the equation is \( y = 2x + 1 \).
  • If \( b = -3 \), the equation is \( y = 2x - 3 \).

In summary, the equation of any line parallel to \( y = 2x + 4 \) can be written as \( y = 2x + b \) where \( b \) is a constant.