# Affine functions

A function is **affine** if it has this algebraic expression: y = f(x) = mx + n (m,n € R), with a polynomial of degree 0 or 1.

Its graph is a straight line, where m is called **slope **and n is called **y-intercept**.

- If m > 0 the function is increasing

- If m < 0 the function is decreasing

Example: f(x) = 3x + 2

3 is the slope and 2 the y-intercept

If we have either 2 points or a point and the slope of an affine function, we can find the algebraic expression.

With two points, we calculate *m* as the average rate of change in this interval and then we get* n* by substituing a point in the formula.

With one point and the slope, we get the* n* as before.

Example: if we have the points (1,1) and (3,4):

**Exercise**: find out these affine functions, knowing that:

a) m=3 and its graph passes through the point (1,-5)

b) Its graph passes through the points (0,3) and (1,1)

Solutions: a) y = 3x - 8; b) y = -2x + 3

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