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

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Let us write the equation for the line:

y-y1 = s (x-x1) where s is the slope.

Given s = 1/2

But we know that:

s= (y2-y1)/(x2-x1)

Given two points ( m, 4 ) and (4, -2)

==> S = (-2-4)/(4-m) = `1/2

==> -6/(4-m) = 1/2

Cross multiply:

==> -6*2 = 4- m

==> m = 4 + 12

**==: m = 16**

The slope s of the line joining the points (x1,y1) and (x2,y2) is given by:

s = (y2-y1)/(x2-x1)...(1)

The slope is given to be 1/2. And the coordinates of the two points are (4,-2) and (m,4).

Substituting these values in formula of the slope we get:

(1/2) = {4-(-2)}/(m-4)

m-4 = 2*6

m = 12+4

m =16

Therefore the value of m = 16 in order that the line joining the points ( 4, -2) and (m , 4) has a slope 1/2.

As the line passes through the points (4 , -2) and (m , 4), its has a slope equal to ( -2 -4) / (4 - m).

Also we are given that it has a slope of 1/2.

Therefore

( -2 -4) / (4 - m) = 1/2

=> -6 / ( 4 - m) = 1/2

=> -6*2 = 4-m

=> -12 = 4-m

=> m= 4+ 12

=> m = 16

**Therefore the required value of m is 16**

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**