Example:  find out the slope of equations and sketch the graph of the line.

                        2 y - 6x = -2

Solution

To get the slope we'll first put this in slope-intercept form and then the slope will simply be the coefficient of the x (with sign). In order to graph the line we know the y-intercept of the line, that's the number without an x (with sign) and as discussed above we can employ the slope to determine a second point on the line.  At that instance there isn't anything to do other than sketch the line.

First solve the equation for y. 

                              2 y = 6 x - 2

                                    y = 3x -1

Thus, the slope for this line is 3 and the y-intercept is the point (0, -1).  Don't forget to take the sign while determining the y-intercept.  Now, to determine the second point usually we like the slope written as a fraction to make it apparent what the rise & run are.  So,

                                 m = 3 = 3/1 = rise /run    ⇒        rise = 3,  run = 1

Then the second point is,

x₂  = 0 + 1 = 1                        y₂  = -1 + 3 = 2   ⇒     (1, 2)

Following is a sketch of the graph of the line.