Question

Find the equation of the line that passes through the two points ( -3,9) and ( -1/2,-7/2).Write your answer in standard form.

Answer 1

Given

The line passes through the points,

$(-3,9),(-\frac{1}{2},-\frac{7}{2})$

To find the equation of the line and write in the standard form.

Now,

The equation of the line passing through two points is given by,

$\frac{y_{}-y_1}{y_2-y_1}=\frac{x_{}-x_1}{x_2-x_1}$

Since the points are

$(-3,9),(-\frac{1}{2},-\frac{7}{2})$

Then, the equation of the line is,

$\begin{gathered} \frac{y-9}{-\frac{7}{2}-9}=\frac{x-(-3)}{-\frac{1}{2}-(-3)} \\ \frac{y-9}{\frac{-7-18}{2}}=\frac{x+3}{\frac{-1+6}{2}} \\ \frac{y-9}{-25}=\frac{x+3}{5} \\ \frac{y-9}{-5}=x+3 \\ y-9=-5(x+3) \\ y-9=-5x-15 \\ y=-5x-15+9 \\ y=-5x-6 \end{gathered}$

Hence, the equation of the line is,

$y=-5x-6$

And, the standard form of the line is,

$5x+y+6=0$