Points (6, -2) and (a, 6) are on the line with a slope of 4/3. What is the value of a ?

We'll write the equation of the line in the standard
form:

y = mx + n, where m is the slope and n is y
intercept.

We know, from enunciation, that the line has the
slope m= 4/3. We'll substitute the value of the slope in the equation of the
line.

y = 4x/3 + n

The point
(6, -2) is located on the line so it's coordinates verify the equation of the
line:

-2 = 4*6/3 + n

-2 = 8 +
n

We'll subtract 8 both
sides:

n = -2 - 8

n =
-10

The equation of the line
is:

y = 4x/3 - 10

The
point  (a, 6) belongs to the same line also. So, it's coordinates belong to the
line.

6 = 4a/3 - 10

We'll add
10 both sides:

4a/3 = 16

4a =
3*16

We'll divide by 4 both
sides:

a = 3*4

a
= 12