Question

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

Answer 1

Answer:

$n=-4$

Step-by-step 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 $[tex]y-1=\frac{4-1}{-2-1}\left ( x- 1\right )$[/tex]

Here, $x_{1} =1, x_{2} =-2,y_{1} =1,y_{2} =4$

So, equation of the line is $y-1=\frac{4-1}{-2-1}\left ( x- 1\right )$

$y-1=\frac{3}{-3}\left ( x- 1\right )$

$y-1=-x+1$

$x+y=2$

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 $-4$.

Answer 2

-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