Question

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

Answer 1

Parallel lines have the same slope. The equation \( y = 2x + 4 \) has a slope of \( 2 \). Therefore, any line parallel to this line will also have a slope of \( 2 \).

The general form of a line's equation is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. Since we want a line that is parallel, its equation will have the form:

\[
y = 2x + b
\]

where \( b \) can be any real number, indicating that there are infinitely many lines parallel to \( y = 2x + 4 \). For example:

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

Any of these equations represents a line parallel to the line \( y = 2x + 4 \).