Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example

Example   Graph y = - 2/5 x + 3 .

Solution: It is a line in the slope intercept form

                                                 y = mx + b

In this the line contain a y intercept of (0,b) and a slope of m.  Remember that slope can be thought of as

                                                          m =rise /run

Note as well that if the slope is -ve we tend to think of the rise as a fall.

The slope let us to get a second point on the line. Once we contain any point on the line and the slope we move right by run & up/down by rise based on the sign. It will be a second point on the line.

In this we know (0,3) is a point on the line and the slope is -2/5.  Thus beginning at (0,3) we'll move 5 to the right (that means 0 → 5 ) and down 2 (that means  3 → 1 ) to get (5,1) as a second point on the line.  Once we've got two points on a line all we have to do is plot the two points & connect them along with a line.

Following is the sketch for this line.