Answer:
3y = 5x - 24
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3y = 5x + 2 ( divide through by 3 )
y = [tex]\frac{5}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{5}{3}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (6, 2 ) into the partial equation
2 = 10 + c ⇒ c = 2 - 10 = - 8
y = [tex]\frac{5}{3}[/tex] x - 8 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = 5x - 24 ← equation of parallel line
