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

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

Let

then

We have the equation of a line:

Convert to the slope-intercept form:

          subtract 2x from both sides

             divide both sides by 3

therefore the slope is

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

           subtract 4/3 from both sides

Finally:

Convert to the standard form (Ax + By = C):

             multiply both sides by 3

          add 2x to both sides

Let .

Lines k and l are parallel iff

We have the equation:

then the equation of a line parallel to given lines has the equation:

Put the coordinates of the point (-2, 3) to the equation:

Finally: