What is an equation of the line that passes through the point (6,7) and is parallel to the line 2x-3y=92x−3y=9?

The equation of the line passing through the point (6, 7) parallel to the line is y = 2/3x + 3

The equation in slope - intercept form :

2x - 3y = 9

-3y = 9 - 2x

Divide both sides by - 3

y = - 3 + 2/3x

Using the points (6, 7)

7 = c + 2/3(6)

7 = c + 12/3

7 = c + 4

c = 7 - 4 = 3

c = 3

The equation of the parallel line is thus :

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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

2 5/8 is the final answer! : )

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step-by-step explanation: