The slope of two parallel lines must be the same; if the slopes of two lines are the same then they must be parallel.

Example 1:

If line y=mx+2 and line y=3x+3 are parallel, what is the value of m?

Answer: Since the slope of two parallel lines must be the same, m=3.

Example 2:

Line 1 in point slope form is y=4x+5 and line 2 is y-9=4(x-7). Are these two lines parallel?

Answer: Yes. Line one is in point slope form y=mx+b, slope m=4.

                      Line two is in the form (y-y1)=m(x-x1), slope m=4, identical slope means they are parallel.