# Linear Function

015B

Question 015A was about Bob and his figurines.  Every month we added 3 figurines to the total number of Bob figurines.  If you look at this, you should notice that the number of figurines increases by 3 each month.  That is a steady linear rise.  The correct answer was Linear.  Let's talk about Linear Functions a bit and then ask question 015B.

## Linear Functions explained

The key part of of the word Linear is the first 4 letters LINE!  These functions form a straight line when plotted on a piece of graph paper.  the equation will be in the form y = ax + b where a and b are constant numbers. Quadratic functions are of the form

y = ax2 + bx + c

when graphed it will form a parabola which looks like this - Exponentials are of the form

y = 3x And they look similar to this.  Growth or decay starts at a point and then rises (or falls) in ever increasing jumps.

And, while we're at it, let's talk a little about Absolute Values.  This is when the portion of the equation within the brackets is positive such as y = | 2x | + 7.  The 2x is positive regardless of what value we let x be.  So, the graph of an absolute value is mirrored about a line representing where the value of the stuff inside the straight line brackets turns to negative and then back to positive by the brackets.  Anyway, for a linear function it looks like this - ## Question 015B!!

Bob is getting better and better at laying bricks.  He gets paid by the brick, and each week he makes 2 more dollars than the previous week.  It's starting to look like he will keep improving at this rate forever!  One could say his skill level increases at a ____________  rate.

a) Linear