Question

For what value of x will the point (x,-1),(2,1) and (4,5) lie on a line

Answer 1

Therefore the value of x is 1.

Step-by-step explanation:

Given, points are (x,-1), (2,1) and (4,5)

A equation of a line which passes through the points $(x_1,y_1)$ and $(x_2-y_2)$ is

$y-y_1=\frac{y_1-y_2}{x_2-x_1} (x-x_1)$

Therefore the equation of line which is passes through the points (2,1) and (4,5) is

$y-1=\frac{5-1}{4-2} (x-2)$                      [$x_1=2,y_1=1 ,x_2=4$ and $y_2=5$]

$\Leftrightarrow y-1 = \frac{4}{2} (x-2)$

$\Leftrightarrow y-1 = 2 (x-2)$

$\Leftrightarrow 2x-y=3$

Since the three points (x,-1), (2,1) and (4,5) lie on a line. Then (x,-1) will be satisfy the above equation of line .

$2x-(-1)=3$

$\Leftrightarrow 2x =3-1$

$\Leftrightarrow 2x = 2$

$\Leftrightarrow x=1$

Therefore the value of x is 1 .

Answer 2

Step-by-step explanation:

hope this two pics will help you.