What is a function?

A function is defined as a relation between a given set of elements known as the domain and another set of elements known as the codomain. The function associates each element in the domain with another element in the codomain. The elements in the relationship may be of any kind of thing including objects, words and qualities but are typical mathematical quantities, like real numbers.

An example f(x) =3x is a function with the real numbers as  its domain and codomain because it  associates every real number with the real number thrice  as big and therefore it can be written as  f(2) = 6   Ruthing, D. (1984).

 What is a linear function?

A linear function is a function that has no exponents other than one and is without products of the variables for instance y=x+2, 2x-4y = 1/4 and y= -2, are all linear. These functions have x as the input variable, and x is raised only to the first power. Such functions yield graphs that are straight lines therefore, the name linear.

What form does a linear function take? (I.e.,What is the standard mathematical notation of a linear function?)

There are three standard forms for linear functions:

The “general form” Ax + By = C (the equation defines y implicitly as a function of x as long as B≠ 0.)

The “Taylor” or “point-slope” form

y – yo = m(x – x0) or, equivalently, f(x) = y0 + m(x – x0) (),

and  The “slope-intercept” form     y = f(x):

f(x) = mx + b (),

In the general form, -A/B is the slope of the line   if B≠ 0 and infinite if B = 0.

If f(x) is linear then the graph of y = f(x) is a straight line. The parameter m in the two formulas is the slope of this line. In the point-slope form, the point (x0, y0) is a point on the line y = f(x). In the slope-intercept form, the parameter b is the y-intercept.

What is the formula for determining the slope of a line?

The slope of a line is the ratio of the change in y over the change in x. the formula for finding the slope of a line is therefore as follows:

m=y₂-y1∕x₂-x₁