How do you determine the slope of a line parallel to y = 4x - 1?

The slope of a line parallel to y = 4x - 1 is 4.

To determine the slope of a line parallel to a given line, you need to look at the coefficient of \( x \) in the equation of the line. The given equation is \( y = 4x - 1 \). This equation is in the slope-intercept form, \( y = mx + c \), where \( m \) represents the slope and \( c \) represents the y-intercept.

In the equation \( y = 4x - 1 \), the coefficient of \( x \) is 4. This means the slope \( m \) is 4. When two lines are parallel, they have the same slope. Therefore, any line parallel to \( y = 4x - 1 \) will also have a slope of 4.

Understanding the concept of parallel lines is crucial. Parallel lines never intersect and always maintain the same distance apart. This is because they have identical slopes. So, if you are given any linear equation and asked to find the slope of a line parallel to it, simply identify the coefficient of \( x \) in the equation. That coefficient is the slope of the parallel line.

For example, if you have another line with the equation \( y = 4x + 3 \), the slope is still 4, making it parallel to \( y = 4x - 1 \). The y-intercept (the constant term) does not affect the slope, so it can be different, but the lines will still be parallel as long as their slopes are the same.