Write an equation in slope intercept form for the line that passes through (-2,3) and is parellel to the line whose equation 3x+2y=6

Parallel lines refers to a pair of straight lines that never intercept or touch each other. The slopes of this lines is the same one.

On this exercise is given the equation of a line and a point, and is asked to find the equation of a line in slope-intercept form that is parallel to the given one, and that passes through the given point. 

3x+2y=6              Subtract 3x in both sides
2y=-3x+6             Divide by two in both sides to isolate y
y=-3/2x+3

The slope of the given line is -3/2, which means that the slope of a line parallel to this one, have to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the slope-intercept form y=mx+b, where letter m represents the slope.

y=mx+b                Substitute the values of the given point and slope
3=(-3/2)-2+b         Combine like terms
3=3+b                   Subtract 3 in both sides
0=b

The equation in slope intercept form for the line that passes through the point (-2,3) and is parallel to the line whose equation is 3x+2y=6 is y=-3/2x or y=-3/2x+0.