To determine the slope of a line that is parallel to the line given by the equation [tex]\( y = 5x + 3 \)[/tex], we need to identify the slope of the given line itself.
First, recall that the equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
In the equation [tex]\( y = 5x + 3 \)[/tex]:
- The coefficient of [tex]\( x \)[/tex], which is 5, represents the slope [tex]\( m \)[/tex].
- The constant term, which is 3, represents the y-intercept [tex]\( b \)[/tex].
Since the slope [tex]\( m \)[/tex] of the line [tex]\( y = 5x + 3 \)[/tex] is 5, any line that is parallel to this line must have the same slope. Parallel lines share identical slopes because they never intersect and always maintain the same distance from each other.
Therefore, the slope of a line that is parallel to the line [tex]\( y = 5x + 3 \)[/tex] is:
[tex]\[ 5 \][/tex]
