Question

Line passing through the point (1,7) that is perpendicular to the line y=-1/9x +6

Answer 1

So first of all, know that perpendicular lines have slopes that are a negative reciprocal from each other. So your original equation is in slope-intercept format: y = mx + b, where m = slope
So your slope is -1/9. Now the negative of that would be --1/9 = +1/9. Now the reciprocal of 1/9 is 9/1 = 9 (you just flip the fractions ;).
Now that we have our new slope, let's make an equation of a line with that new slope and the point (1, 7). For that let's switch to the point-slope format: y-k = m(x-h), where h = the x-value and k = the y-value.
Our h = 1 and k = 7
y-7 = 9(x-1)