5x + 8y = 60
the equation of a line in ' slope-intercept form ' is
y = mx + c → (m is the slope and c the y-intercept)
rearrange 5x + 8y = 120 into this form
subtract 5x from both sides
8y = - 5x + 120
divide all terms by 8
y = - [tex]\frac{5}{8}[/tex] x + 15 ( in slope-intercept form)
hence slope m = - [tex]\frac{5}{8}[/tex]
Parallel lines have equal slopes
thus partial equation is
y = - [tex]\frac{5}{8}[/tex] x + c
to find c substitute (4, 5) into the partial equation
5 = - [tex]\frac{5}{2}[/tex] + c ⇒ c = [tex]\frac{15}{2}[/tex]
y = - [tex]\frac{5}{8}[/tex] x + [tex]\frac{15}{2}[/tex]
multiply through by 8
8y = - 5x + 60 ⇔ 5x + 8y = 60 → (equation of parallel line)
