How do you determine if a pair of lines are parallel? For example, the lines -3x+8y=24 and 3x-8y=7?
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If we are to write this equation in slope-intercept form, it will be in y = mx + b, where m is the slope of the line and b is the y intercept. We need then to find the slope of the line using 2 points on the line and filling in the slope formula to find the slope. One of the points we can use is (0, 3) which is also the y intercept. The y-intercept is found where x = 0. Where x = 0, y = 3. So b = 3. Now for the slope we will use (0,3) and (4,4): 
. Using that m value and that b value we have the equation 
. There you go!