mCalculate the value of m if the points (4,-2) and (m,4) are on the line with the slope 1/2.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to notice that the problem provides the information that the line passes through the points `(4,-2)` and `(m,4)` and it has the slope `m = 1/2` , hence, you may use slope equation, such that:

`m = (y_2-y_1)/(x_2-x_1)`

Considering `(x_1,y_1) = (m,4)` and `(x_2,y_2) = (4,-2)` yields:

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

You need to perform cross multiplication such that:

`-6*2 = 4 - m => -12 = 4 - m => m = 12 + 4 => m = 16`

Hence, evaluating the missing coordinate m yields `m = 16` .

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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