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Sagot :
Answer:
3y = 2x + 3
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 = 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 (6, 5 ) into the partial equation
5 = 4 + c ⇒ c = 5 - 4 = 1
y = [tex]\frac{2}{3}[/tex] x + 1 ( multiply through by 3 to clear the fraction )
3y = 2x + 3 ← equation of parallel line
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