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.