Question

Write an equation of the line passing through the given points(1,3) and (-1,-9)

Answer 1

The Solution:

Given:

`(1,3)\text{ and }(-1,-9)`

Required:

To find the equation of a line passing through the given points.

By the formula for the equation of a line:

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \\ \text{ In this case,} \\ x_1=1 \\ y_1=3 \\ x_2=-1 \\ y_2=-9 \end{gathered}`

Substitute these values in the formula.

`\begin{gathered} (y-3)/(x-1)=(-9-3)/(-1-1) \\ \\ (y-3)/(x-1)=(-12)/(-2) \\ \\ (y-3)/(x-1)=6 \end{gathered}`

Cross multiply to get:

`\begin{gathered} y-3=6(x-1) \\ \\ y-3=6x-6 \\ y-6x-3+6=0 \\ y-6x+3=0 \end{gathered}`

Therefore, the correct answer is:

`\begin{gathered} y-6x+3=0 \\ \text{ Which is the same equation as:} \\ y=6x-3 \end{gathered}`