To find the slope of a line that is parallel to the line given by the equation [tex]\( y = 5x + 3 \)[/tex], we need to understand the properties of parallel lines. Two lines are parallel if and only if they have the same slope.
First, recall that a linear equation in the 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 given equation:
[tex]\[ y = 5x + 3 \][/tex]
we can see that it is already in the slope-intercept form. Here, the coefficient of [tex]\( x \)[/tex] (which is 5) is the slope of the line.
Therefore, for any line to be parallel to this given line, it must have the same slope. Thus, the slope of a line that is parallel to [tex]\( y = 5x + 3 \)[/tex] is:
[tex]\[ 5 \][/tex]
