For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut point with the y axis
We have the following equations:
Equation 1:
[tex]-5x + 6y = -9\\6y = 5x-9\\y = \frac {5} {6} - \frac {9} {6}\\y = \frac {5} {6} - \frac {3} {2}[/tex]
By definition, if two lines are perpendicular then the product of their slopes is -1:
[tex]-1 = \frac {5} {6} * m_ {2}\\m_ {2} = - \frac {6} {5}[/tex]
Equation 2:
[tex]-8x-9y = -8\\9y = -8x + 8\\y = \frac {-8x} {9} + \frac {8} {9}\\y = - \frac {8} {9} x + \frac {8} {9}[/tex]
Finally, the requested equation is:
[tex]y = - \frac {6} {5} x + \frac {8} {9}[/tex]
Answer:
[tex]y = - \frac {6} {5} x + \frac {8} {9}[/tex]
