Answer: [tex]y = \frac{2x}{3} - \frac{11}{3}[/tex]
Step-by-step explanation:
Equation of the line given ;
[tex]2x - 3y = 9[/tex]
To find the slope of the line we will make y the subject of formula , that is
[tex]3y = 2x - 9[/tex]
[tex]y = \frac{2x}{3}-3[/tex]
Therefore ; the slope = [tex]\frac{2}{3}[/tex]
Two lines are said to be parallel if they have the same slope
This means that the slope of the second line = [tex]\frac{2}{3}[/tex]
Using the formula [tex]y-y_{1}= m ( x - x_{1} )[/tex] to find the equation of the line , we have
[tex]y - (-1 ) = \frac{2}{3} (x - 4 )[/tex]
[tex]y + 1 = \frac{2x}{3} -\frac{2}{3}(4)[/tex]
[tex]y + 1 = \frac{2x}{3} - \frac{8}{3}[/tex]
[tex]y = \frac{2x}{3}- \frac{8}{3} - 1[/tex]
[tex]y = \frac{2x}{3} - \frac{11}{3}[/tex]
