As my math teacher would say, the Math gods just picked those random variables to represent these things. There is no specific reason to my knowledge.
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There is no slope nor intercept because there is no equation, simply an expression.
first of all, i dont see how slope and yintercept has anything to do with shopping. usually in an equation, y= mx+b, m stands for slope, and b is the y-intercept. x and y are just x and y. If the equation is mixed up, and is not in y=mx+b format, you need to solve to get y on one side, the slope, x, and whatever the presented constant is (which is the y-intercept) on the other side. hope this helps.
y=mx+b m=slope b=y-intercept
Given a point P = (a,b) and slope m, the equation of a line through P with slope m is (y-b) = m(x-a)
Given a point P(a,b) and slope m, the point slope equation is (y - b)/(x - a) = m