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