A line passes through (6, 3), (8, 4), and (n, -2). Find the value of n.

Question

A line passes through (6, 3), (8, 4), and (n, -2). Find the value of n.

Answer 1

We have a line passing through 3 points.  We can use the first

two points to find the equation of the line.

(6,3), (8,4)

 

slope m = (4-3)/(8-6) = 1/2

 

We can use the point slope form  y-y₁ = m(x-x₁) or

the slope intercept form y = mx + b  

to find the equation of the line.

 

Let's take the point (6,3) and use y = mx + b to find b

y = 3, x = 6, m = 1/2

 

3 = (1/2)(6) + b

3 = 3 + b

0 = b

 

The equation of our line is   y = (1/2)x

 

We have a line of equation y = (1/2)x going through point (n,-2) 

 

Plugging in we have:  -2 = (1/2)n

                                2(-2) = n

                                -4 = n

 

Your answer is  n = -4

 

NOTE:  looking at the 3 points as given initially: (6,3), (8,4), (n,-2)

We can see that 3 = (1/2)6  and  4 = (1/2)8   so  -2 = (1/2)n makes sense

 

Hope this helps

Answer 2

If a line passes through any given points, then it will have the same slope for any pair of coordinates on that line.

 

i.e., (4-3)/(8-6) = (-2-4)/(n-8)   where, slope of a line = (y_{2 -} y₁) / (x₂ - x1)

Answer 3

You can assume that those three points are A, B, and C, then this line passes through A, B, and C, which means the slope of AB equals to the slope of BC. Now you can form your formula by using that fact.