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

Answer:

m =  5

Step-by-step explanation:

P(2, 3)  ; Q(3 ,6)  ; R(m , 12)

Slope of QR = slope of PQ

Slope of PQ:

$slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

        $= \frac{6-3}{3-2}\\\\=\frac{3}{1}\\\\=3$

Slope of QR:

Slope = $\frac{12-6}{m-3}$

          $=\frac{6}{m-3}$

Slope of PQ = slope of QR

$3=\frac{6}{m-3}\\\\3*(m-3)=6\\\\3m - 9 = 6$

        3m = 6 + 9

        3m = 15     {Divide both sides by 3}

     3m/3 = 15/3

m = 5

Answer 2

Answer:

m = 5

Step-by-step 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 = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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

m = $\frac{6-3}{3-2}$ = $\frac{3}{1}$ = 3

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

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

m = $\frac{12-6}{m-3}$ = $\frac{6}{m-3}$ = 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