The slope of the line passing through the points (x,4) and (4,6) is m=2. What is x?

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

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

We know, from enunciation, that the line has the
slope m= 2. We'll substitute the value of the slope in the equation of the
line.

y =2x + b

The point (4,
6) lies the line if and only if it's coordinates verify the equation of the
line:

6 = 2*4 + b

6 = 8 +
b

We'll subtract 6 both sides and we'll apply the symmetric
property:

b = 6 - 8

b =
-2

The equation of the line
is:

y = 2x - 2

The point  (x,
4) lies on the given line if and only if it's coordinates verify the equation of the
line.

4 = 2x -  2

We'll add 2
both sides:

2x = 4+2

2x =
6

x = 3

The
missing coordinate is x = 3.