Question

A line passes through (1,1) , (-2,4) , and (6,n) . Find the value of n.

Answer 1

-4.

The equation for a line is y-y₁=m(x-x₁)
Using the following:
x₁= 1
x₂= -2
y₁= 1
y₂= 4

and slope, or m, is (x₂-x₁)/(y₂-y₁),

You can now fill out the equation!
y-(1)=-1(x-(1))
y= -x+2

And solve by substituting the 6, or x₃, into the equation to find the corresponding y value:

y= -(6)+2
y= -4

Therefore,
n=-4

Answer 2

`n=-4`

Explanation:

The line passes through the points
`\left ( 1,1 \right ),\:\left ( -2, 4\right ),\:\left ( 6,n \right )`

We know that equation of a line passing through two given points
`\left ( x_(1),y_(1) \right )` and
`[tex]y-1=(4-1)/(-2-1)\left ( x- 1\right )`[/tex]

Here,
`x_(1) =1, x_(2) =-2,y_(1) =1,y_(2) =4`

So, equation of the line is
`y-1=(4-1)/(-2-1)\left ( x- 1\right )`

`y-1=(3)/(-3)\left ( x- 1\right )`

`y-1=-x+1`

`x+y=2`

So, the equation of the line is
`x+y=2`.

As, the point
`(6,n)` lies on the line, will satisfy the equation of the line.

`6+n=2\:\:\left [\because x=6,y=n\right ]`

`n=-4`

Hence, the value of n is
`-4`.