# What is the equation of the line that passes through (2,-7) and parallel to 3x+6y -8 = 0

hala718 | Certified Educator

We need to find the equation of the line that passes through the point (2, -7)

==> y-y1 = m(x-x1)

==> y+ 7 = m(x-2)

Now we will find the slope.

We know that the line if parallel to 3x+6y -8 = 0

Then, we know that the slopes are the same.

==> We will rewrite into the slope form.

==> y= (-1/2)x + 4/3

Then the slope is m= -1/2

==> y+7 = -(1/2)(x -2)

==> y= (-1/2)x + 1 - 7

==> y= -1/2 x - 6

==> 2y = -x - 12

The equation of the line is x + 2y + 12 = 0

justaguide | Certified Educator

The slope of two parallel lines is equal.

For the line 3x + 6y - 8 = 0, the slope can be found by writing it in the slope-intercept form y = mx + c, where m is the slope.

3x + 6y - 8 = 0

=> 6y = -3x + 8

=> y = (-3/6)x + 8/6

m = -1/2

The slope of the required line is -1/2.

As it passes through (2, -7), the equation of the line is:

(y + 7)/(x - 2) = -1/2

=> 2y + 14 = 2 - x

=> x + 2y + 12 = 0

The equation of the required line is x + 2y + 12 = 0