An equation of a line in slope-intercept form that passes through (3, 2) and is perpendicular to the graph of 4x – 3y = 12

Slope intercept form of a linear equation: y = mx + b. (1)

and is perpendicular to the graph of 4x – 3y = 12  (2)

Rewrite (2) in a slope-intercept form:

4x – 3y = 12→→ -3y = -4x+12 →→ y = 4x/3 - 3 (3)
The coefficient m of (3) = 4/3, that means the coefficient of any line perpendicular to (3) is -3/4 ( m.m' = -1)

Now let's go back to (1). We know that this line passes through (3,2) and we also know that its coefficient is -3/4,
Then plug in x & y in (1)→→ 2=-3/4(3) + b and b = 13/4

And the final equation becomes :

y = -3/4(x) + 13/4