Question

What is an equation of the line that passes through the point (-6,-4) and is parallel to the line 3y=2x-6

Answer 1

Answer:

y  =  $\frac{2}{3}$x

Explanation:

Given parameters:

  Coordinates  = (-6, -4)

   Equation of a the line; 3y = 2x - 6

Unknown:

Equation of the line parallel to this line  = ?

Solution:

The equation of any straight line is expressed as;

              y  = mx  + c

y and x are the coordinate

 m is the slope  

c is the intercept of the y - axis

Now from the equation, let us find the slope;

   3y = 2x - 6

     y  = $\frac{2}{3} x$ - $\frac{6}{3}$

    y  =  $\frac{2}{3} x$ - 2

The slope is  $\frac{2}{3}$

Parallel lines are lines that never meets. Therefore they have the same slope;

  the slope of the new line is  $\frac{2}{3}$

Now,

  for the new line, we need to find the intercept;

        since y = mx + c,

     y  = -4 and x = -6;

           -4 =  $\frac{2}{3}$ x (-6) + c

          - 4  = -4 + c

           c= 0

The equation of the new line is;

            y  =  $\frac{2}{3}$x