they are used in equations to find the roots and in equations to find the minimum / maximum point of a quadratic equation and in equations to find the slope and y-intercept of a straight line, among other uses that I am probably not totally aware of.
in a quadratic equation, the formula to find the roots is called the quadratic formula and it is:
the quadratic equation itself is (standard form) ax^2 + bx + c = 0 where:
a is the coefficient of the x^2 term
b is the coefficient of the x term
c is the constant term
you use the a,b,c terms in the quadratic formula to find the roots.
the minimum / maximum point of the quadratic equation is given by the formula:
x = -b/2a
once again, it's the coefficients that are used in this formula.
b is the coefficient of the x term.
a is the coefficient of the x^2 term.
In a straight line, the standard form of the equation is ax + by = c where:
a is the coefficient of the x term
b is the coefficient of the y term
c is the constant term
the slope-intercept form of the equation of a straight line is y = mx + b where:
m is the slope
b is the y-intercept
to convert from the standard form of the equation of a straight line to the slope-intercept form of the equation for a straight line, solve for x.
ax + by = c is the standard form.
subtract ax from both sides of this equation to get:
by = -ax + c
divide both sides of this equation by b to get:
y = (-a/b)*x + (c/a)
your slope of m is equal to (-a/b)
your y-intercept of b is equal to (c/a)
no relationship between b in the slope-intercept form of the equation to the b which is the coefficient of the x term.
they really should have used another letter to represent the y-intercept but they didn't so some confusion can occur although you are mostly working with numbers to the problem doesn't come up as it did now.
anyway, some very smart people figured out these formulas that are very ueful to solve these types of equations.
