find an equation of the line that passes through the point (3, 2) and is perpendicular to the line 8x + 7y − 9 = 0. (let x be the independent variable and y be the dependent variable.)
( show each step and you for your time)

1) first we have to find the slope of the linear function we have to find. As we know, it is perpendicular to the function 8x+7y-9=0. So that means that the slope of our function has to be opposite and inverse to the function we are given. To know the slope of the function we have to isolate Y.

8x+7y-9=0
7x=-8x+9
X=-8/7x+9/7

So the slope of this function is -8/7, which means that the slope of our function is 7/8.

So far we know that:
Y=7/8x+B

2) now we have to find the value of the intersection with Y (B). In order to do this we use the point (3;2) and supplant it on the equation.

2 = 7/8 . 3 + b

2 = 21/8 + b

2 - 21/8 = b

-5/8 = b

So the equation is:

Y = 7/8 x - 5/8

I hope you find my answer helpful