Find the equation of value 'a' if the perpendicular distance from (3,a) to the line 3x+4y-9=0 is 4?

To find the equation of value 'a', we need to find the equation of the line perpendicular to the line 3x + 4y - 9 = 0 passing through the point (3, a).

First, let's find the slope of the given line. The equation of the line can be rewritten in slope-intercept form as y = (-3/4)x + 9/4. The slope of this line is -3/4.

The slope of a line perpendicular to this line is the negative reciprocal of -3/4, which is 4/3.

Now, let's find the equation of the line passing through (3, a) with a slope of 4/3. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the point (3, a) and m is the slope 4/3.

Substituting the values, we have:

y - a = (4/3)(x - 3)

Expanding and rearranging the equation, we get:

y - a = (4/3)x - 4

Adding 'a' to both sides of the equation, we have:

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

Therefore, the equation of value 'a' is y = (4/3)x - 4 + a.