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]
Read more about equations of parallel lines at:
https://brainly.com/question/402319
