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