For the given condition of lines to be parallel, slope of red line is same as green line which is equal to [tex]\frac{-3}{7}[/tex].
" Parallel lines are defined as the lines in the same plane with equal distance between them and do not intersect in the same plane."
" Slope is defined as the ratio of increment in the y-coordinates to the x-coordinates."
Condition of slope for two parallel lines
[tex]y = m_{1} x + c_{1}\\\\y = m_{2} x + c_{2}[/tex]
[tex]m_{1}[/tex] and [tex]m_{2}[/tex] represents the slope of parallel lines.
As slope of parallel lines always equal.
Therefore,
[tex]m_{1} = m_{2}[/tex]
According to the question,
Given,
The slope of the green line [tex]= \frac{-3}{7}[/tex]
Condition given,
Lines are parallel.
Using the condition of slope of parallel lines we have,
The slope of the parallel lines is always equal.
Therefore,
The slope of the red line [tex]= \frac{-3}{7}[/tex]
Hence, the slope of the red line [tex]= \frac{-3}{7}[/tex] as per the given lines is parallel.
Learn more about parallel lines here
brainly.com/question/16701300
#SPJ2
