Example: find out the slope of equations and sketch the graph of the line.
2 y - 6x = -2
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.