Question

A line passes through (3,5) and (6, 14). What is the equation of the line in point-slope form? O A. y - 5 = 1/3 (x – 3) or y – 14 = 1/3 (x – 6) B. Y- 5 = 3(x – 3) or y – 14 = 3(x – 6) C. y-5 = 19/9 (x – 3) or y – 14 = 19/9 (x – 6) or y - 5 = 9/19 (x – 3) or y – 14 = 9/19 (x – 6)​

Answer 1

B.) y-5 = 3(x-3) or y-14 = 3(x-6)

Answer 2

The equation of line in point slope form is (y - 5) = 3(x - 3) or (y - 14) = 3(x - 6) passing through ( 3 , 5) and (6,14).

What is line ?

" A line is defined as the collection of points in one dimensional plane which represents only one dimension length and can extends to infinity."

Formula used

Slope(m) = $y_{2} - y_{1}$/$x_{2} - x_{1}$

Equation of line : ($y$ - $y_{1}$) = m($x$ - $x_{1}$)

According to the question

We have

($x_{1}$, $y_{1}$) = (3 , 5)

($x_{2}$ , $y_{2}$) = (6 , 14)

Substitute the value in the formula  to get slope of line we get,

 m =  14 - 5/6 - 3

      = 9/3

      = 3

Substitute the value in the formula of equation of line we get,

For ($x_{1}$, $y_{1}$) = (3 , 5)

(y - 5) = 3(x - 3)

or

For ($x_{2}$ , $y_{2}$) = (6 , 14)

(y - 14) = 3(x - 6)

Hence, Option (B) is the correct answer.

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