Question

What is the value of m,the points (2,3),(3,6)and (m,12) are collinear....Please y'all help me out

Answer 1

m = 5

Explanation:

Since the points are collinear, they all lie on the same line and have the same slope between them.

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (3, 6)

m =
`(6-3)/(3-2)` =
`(3)/(1)` = 3

Now calculate the slope using 2 other points and equate to 3

(x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (m, 12)

m =
`(12-6)/(m-3)` =
`(6)/(m-3)` = 3 ( multiply both sides by m - 3 )

6 = 3(m - 3) ← divide both sides by 3

2 = m - 3 ( add 3 to both sides )

5 = m

Answer 2

m = 5

Explanation:

P(2, 3) ; Q(3 ,6) ; R(m , 12)

Slope of QR = slope of PQ

Slope of PQ:

`slope = (y_(2)-y_(1))/(x_(2)-x_(1))`

`= (6-3)/(3-2)\\\\=(3)/(1)\\\\=3`

Slope of QR:

Slope =
`(12-6)/(m-3)\\`

`=(6)/(m-3)`

Slope of PQ = slope of QR

`3=(6)/(m-3)\\\\3*(m-3)=6\\\\3m - 9 = 6\\\\`

3m = 6 + 9

3m = 15 {Divide both sides by 3}

3m/3 = 15/3

m = 5