What is the equation of a line parallel to 2x−3y=5 that passes through the point (−9,2)?


3x−2y=−31

3x+2y=−23

2x−3y=−24

2x+3y=−12

Parallel lines have the same slope

The equation of the line is: [tex]\mathbf{y = \frac 23x + 8}[/tex]

From the question, we have:

[tex]\mathbf{2x - 3y = 5}[/tex]

Make y the subject

[tex]\mathbf{- 3y = 5 - 2x}[/tex]

Divide through by -3

[tex]\mathbf{y = \frac 23 x - 5}[/tex]

Because the required equation is parallel to [tex]\mathbf{2x - 3y = 5}[/tex], then they must have the same slope

A linear equation is represented as:

[tex]\mathbf{y=mx + c}[/tex]

Where:

m represents the slope

So, by comparison:

[tex]\mathbf{m = \frac 23}[/tex]

This means that:

The required equation has a slope of 2/3

The equation of the line is:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

Where:

[tex]\mathbf{m = \frac 23}[/tex]

[tex]\mathbf{(x_1,y_1) = (-9,2)}[/tex]

So, we have:

[tex]\mathbf{y = \frac 23(x + 9) + 2}[/tex]

Open brackets

[tex]\mathbf{y = \frac 23x + 6 + 2}[/tex]

[tex]\mathbf{y = \frac 23x + 8}[/tex]

Hence, the equation of the line is: [tex]\mathbf{y = \frac 23x + 8}[/tex]

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