Respuesta :
Given:
The equations are
[tex]5y=2x-5[/tex]
[tex]5y=4+3x[/tex]
[tex]5y-3x=-1[/tex]
To find:
The two parallel lines.
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Isolate variable y in each of the given equations, to get the slope intercept form of the lines.
The slope intercept forms of given lines are
[tex]y=\dfrac{2}{5}x-1[/tex]
[tex]y=\dfrac{4}{5}+\dfrac{3}{5}x[/tex]
[tex]y=-\dfrac{1}{5}+\dfrac{3}{5}x[/tex]
On comparing these equations with slope intercept form, we get
Slope of I line = [tex]\dfrac{2}{5}[/tex]
Slope of II line = [tex]\dfrac{3}{5}[/tex]
Slope of III line = [tex]\dfrac{3}{5}[/tex]
Slope of parallel lines are equal. So, lines II and III are parallel because their slopes are equal.
Therefore, the correct option is C.
