Answer:
2x + 3y = 6
Step-by-step explanation:
The equation of a line in slope- intercept fprm is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = 5 ( subtract 2x from both sides )
3y = - 2x + 5 ( divide terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, 1 ) into the partial equation
1 = - 2 + c ⇒ c = 1 + 2 = 3
y = - [tex]\frac{2}{3}[/tex] x + 3 ( multiply through by 3 to clear the fraction )
3y = - 2x + 6 ( add 2x to both sides )
2x + 3y = 6 ← equation of parallel line
