Find the value of m if the points (4,-2) and (m,4) are on the line whose slope is 1/2

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= 1/2. We'll substitute the value of the slope in the equation of the
line.

y = x/2 + n

The point
(4, -2) is located on the line if and only if it's coordinates verify the equation of
the line:

-2 = 4/2 + n

-2 = 2
+ n

We'll subtract 2 both sides and we'll apply the
symmetric property:

n = -2 -
2

n = -4

The equation of the
line is:

y = x/2 - 4

The
point  (m, 4) belongs to the same line if and only if it's coordinates belong to the
line.

4 = m/2 -  4

We'll add 4
both sides:

m/2 = 8

m =
8*2

m =
16