Question

Please I need help on this question, A line passes through (6,3), (8,4), and (n,-2). Find the value of n.

Answer 1

Explanation:

Given that the line passes through

(6,3), (8,4), and (n,-2).

We have to find the value of n.

Let us name the points as A, B and C in that order

Slope of AB = slope of BC since all 3 points lie in the same line

To find slope of AB:

Slope = (y2-y1)/(x2-x1) = (4-3)/(8-6) = 1/2

To find slope of BC:

Using the same formula slope = (-2-4)/(n-8) = -6/(n-8)

The two slopes are equal.

Hence 1/2 = -6/(n-8)

n-8 = -12

n = -4

Answer 2

n= -4

Explanation:

First we have to find the equation of line which passes through (6,3) and (8,4).

Then we have to pass this line through the point (n , -2).

we know, equation of line passing through (x1,y1) and (x2,y2) is

`(x-x1)/(x1-x2)=(y-y1)/(y1-y2)`

So, the equation of line passing through (6,3) and (8,4) is

`(x-6)/(6-8)=(y-3)/(3-4)`

or,
`(x-6)/(-2) =(y-3)/(-1)`

multiplying both sides by -2

x-6=2(y-3)

or, x-6=2y-6

or, x-2y=6-6

or, x-2y=0

Now, we have to pass this line through (n,-2)

So, using the point in the line, that is using x=n , y=-2

we get

n-2(-2)=0

or, n+4=0

or, n=-4