QuestionFind the equation of the line parallel to $12 x-18 y=-36$ that goes through the point $P(-3,-6)$ .

Studdy Solution

STEP 1

Assumptions1. The given line equation is $12x -18y = -36$ . The line we want to find is parallel to the given line3. The line we want to find passes through the point $(-3, -6)$

STEP 2

The general form of a line is $Ax + By = C$ . The given line can be written in this form as $12x -18y = -36$ .

STEP 3

A line parallel to the given line will have the same coefficients $A$ and $B$ (slope), but a different $C$ . So the equation of the line we want to find can be written as $12x -18y = C$ .

STEP 4

To find the value of $C$ , we substitute the coordinates of the point $(-3, -6)$ into the equation.
$12(-3) -18(-6) = C$

STEP 5

Calculate the value of $C$ .
$C =12(-3) -18(-) = -36 +108 =72$

STEP 6

Substitute $C$ back into the equation of the line to get the final equation.
$12x -18y =72$ So, the equation of the line parallel to the given line and passing through the point $(-3, -6)$ is $12x -18y =72$ .

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