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:

$\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ In this case,} \\ x_1=1 \\ y_1=3 \\ x_2=-1 \\ y_2=-9 \end{gathered}$

Substitute these values in the formula.

$\begin{gathered} \frac{y-3}{x-1}=\frac{-9-3}{-1-1} \\ \\ \frac{y-3}{x-1}=\frac{-12}{-2} \\ \\ \frac{y-3}{x-1}=6 \end{gathered}$

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:

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