How to tell if a function is linear? A linear function is a function of f : ℝ→ℝ defined as f(x) = a.x, where a is a real number and a ≠ 0. The linear function is a particular case of the affine function f(x) = a.x + b, where b = 0.
The a number that multiplies by x, is called the coefficient of the function. When the coefficient = 1, the linear function will be called as the identity function, f(x) = x
So, to write a linear function in its standard form would be something like f(x) = a.x.
What does a linear function graph look like?
The graph of a linear function is a straight line that crosses the origin, thus, the point (0, 0). The a coefficient indicates the slope or steepness of the line. the higher de a coefficient, the more steep the graph line will be.