In class, we discussed how toget the equation of a line from the graph, and why this method makessense. We started by looking atsome graphs, and identifying easy points where we could find input-output or x-yvalues to record in a table:

We then found the step size:+2, and noticed that it was the same every time. You can also see step size on the graph:

We did this for a lot ofexamples, A few will follow.

We noted that you could getall of the values in the table by taking a start value (1 in this case) andadding the step size the right number of times; so to get the output for 3, wecould do: 1+2+2+2=1+2*3, and toget the output for 4: we could do 1+2+2+2+2=1+2*4, so the equation would be

y=1+2x.

Notice that the step size ismultiplied by x in the equation: that will be a general pattern.

Example 2: a negative stepsize

Table with step size:

Again, you could get all ofthe values in the table by taking the output at 0 (7 in this case) and addingthe step size the right number of times; so to get the output for 3, we coulddo: 1-3-3-3=1-3*3, so the equationwould be

y=7-3x=-3x+7.

Notice that the step size ismultiplied by x in the equation

Here’s a picture of thestep size on the graph:

Example 3: a fractional stepsize and start value:

To find the values at 0 and 1you need to know that you are evenly dividing everywhere: -1, 0, 1, 2 areevenly spaced (3 spaces), and so are the y-values they go with:

So there are 4 points, with 3even spaces between them that show outputs. The total space is 2, so each of the outputs have to bespaced at 2/3:

Following the same pattern asbefore, the function is:

y = (-2/3)x + 2 1/3