The formula of a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. In this form, you can easily determine the slope of the line as the variable "m". For example. Rewrite 4y - 12x = 20 and y = 3x -1. The equation 4y - 12x = 20 needs to be rewritten with algebra while y = 3x -1 is already in slope-intercept form and does not need to be rearranged. Oftentimes, the formula of the line you are given will not be in slope-intercept form. It only takes a little math and rearranging of variables to get it into slope-intercept.  For example: Rewrite line 4y-12x=20 into slope-intercept form. Add 12x to both sides of the equation: 4y – 12x + 12x = 20 + 12x Divide each side by 4 to get y on its own: 4y/4 = 12x/4 +20/4 Slope-intercept form: y = 3x + 5. Remember, when two lines are parallel to each other, they will have the exact same slope. Using the equation y = mx + b where m is the slope of the line, you can identify and compare the slopes of two lines.  In our example, the first line has an equation of y = 3x + 5, therefore it’s slope is 3. The other line has an equation of y = 3x – 1 which also has a slope of 3. Since the slopes are identical, these two lines are parallel. Note that if these equations had the same y-intercept, they would be the same line instead of parallel.

Summary:
Define the slope-intercept formula of a line. Rewrite the formula of the line in slope-intercept form. Compare the slopes of each line.