Answer:
y = ²/₃x + 3
Step-by-step explanation:
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
Changing to slope-intercept form:
2x - 3y = 9 {subtract 2x from both sides}
-3y = -2x + 9 {divide both sides by (-3)}
y = ²/₃x - 3 ⇒ m₁=²/₃ ⇒ m₂=²/₃
The line y=²/₃x+b passes through point (6, 7) so the equation:
7 = ²/₃×6 + b is true
7 = 4 + b
b = 3
Therefore equation in slope-intercept form:
y = ²/₃x + 3
