What is the equation of the line that crosses the y-intercept at 12 and perpendicular to 7x + 6y = 17?

Let's find the slope to   7x + 6y = 17

The slope in the form Ax + By = C  is    -A / B

So....the slope is  -7 / 6

And a perpendicular line to this will have negative reciprocal slope =    6/7  = m

And  if this perpendicular line has a y intercept of 12....the point (0, 12) is on the line = (x1, y1)

So...the equation is

y = m ( x - x1) + y1         fill in what we know

y = (6/7) ( x - 0 ) + 12

y = (6/7)x + 12

Here's a graph : https://www.desmos.com/calculator/oyd29rauvm