The correct option is (a) i.e. the slope intercept form of the given line is y = 6x-14.

The slope of the line through two points (x₁ ,y₁) and (x₁ ,y₂) can be found by using the formula below.

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, ‘m’, and ‘b’ as the y-intercept can be given as y = mx + b.

Here we have a line that passes through two points (x₁ ,y₁) = (3 ,4) and  (x₁ ,y₂) =(5 ,16).

The slope of the line m = (y₂ – y₁) / (x₂ – x₁) = (16 -4) /(5 -3) = 12/2 = 6.

 ⇒ slope m = 6.

And we know the slope intercept form  is

  y = mx + b

⇒ 4 = 6*3 + b  {with points  (3 ,4)}

⇒ b =4 – 18 = -14 ⇒ b = -14.

So the slope intercept form is y = 6x-14.

The slope-intercept form of the equation with m =6 and y-intercept as -14 was found to be

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope intercept form equation of the line that passes through (3 ,4)and (5,16)?

(a) y = 6x − 14  

(b) y = −6x +14

(c) y = −6x − 14

(d) y = 6x + 14?