How do you determine the slope of a line parallel to y = -4x + 3?

The slope of a line parallel to y = -4x + 3 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 equation \( y = -4x + 3 \) is in the slope-intercept form, which is \( y = mx + c \), where \( m \) represents the slope and \( c \) represents the y-intercept. In this case, the slope \( m \) is -4.

Parallel lines have the same slope because they never intersect and always maintain the same distance apart. Therefore, any line that is parallel to \( y = -4x + 3 \) will also have a slope of -4. This means that if you see another line with the equation \( y = -4x + b \) (where \( b \) can be any number), it will be parallel to the original line because the slope remains -4.

Understanding this concept is crucial for solving problems involving parallel lines. For example, if you are asked to find the equation of a line parallel to \( y = -4x + 3 \) that passes through a specific point, you would start by using the slope -4 and then use the point to find the y-intercept. This ensures that the new line maintains the same slope as the original, confirming that they are indeed parallel.