y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = [tex]\frac{2}{5}[/tex] x - 6 is in this form with slope m = [tex]\frac{2}{5}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{2}{5}[/tex] x + c is the partial equation of parallel line
to find c , substitute (- 1, 5 ) into the partial equation
5 = - [tex]\frac{2}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex] ← equation of parallel line
