How do you put a table in slope intercept form?

Answer 1

In order to 'convert' values from the x-y table to an equation (slope-intercept form), you must have plenty of practice recognizing patterns.

It is crucial to be able to draw connections between x and y values. If you can do this, you are almost done! Sometimes, though, it is impossible to do this just by intuition if the x-y table depict a function or values that are related by complicated formulas. So, do be aware that putting x-y table values into a formula can become extremely complicated.

To illustrate the basic concept of this, though, let us start with something simple.

X | 1 2 3 4 5

Y | 0 2 4 6 8

You can see a pattern for both X and Y values. For example, the X values consecutively increase by a value of 1. eg. 1, 2, 3, 4, 5...etc. Meanwhile, the Y values consecutively increase by a value of 2.

Now it is so crucial to be able to understand the connection between X and Y values. In this case, as X value increases by 1, the Y value increases by 2.

Also, an additional hint is given to us: an x-intercept at 1. Because the y-value at x=1 is 0, we know for certain that 1 is the x-intercept.

If you continue the pattern -based on the rules of the patterns that we've noticed- the table becomes something like this:

X | 0 1 2 3 4 5

Y | -2 0 2 4 6 8

We now know that there exists a y-intercept at 0. What slope-intercept formula gives us a y-intercept at 0 and x-intercept at 1?

Since for every x value, y value increases by 2, the slope is 2.

slope = change in rise / change in run.

The slope-intercept form: y = ax + b. a is now 2 since the slope is 2.

y = 2x + b. Now we need to find out what b is. Since we know many values (from the table) that satisfy this 'connection,' 'pattern,' we can plug in any value from the table into the equation. Let us use (x= 0, y= -2).

Substituting these values, the formula becomes -2 = 2(0) + b.

b = -2.

The formula becomes y = 2x - 2.

Easier Method: If you know that the relationship between x and y values is a linear one, you can substitute a pair of x-y value into the equation y = ax + b after you figure out the slope without worrying about x and y intercepts.

Warning: The reason that I took the long way of explaining x, and y-intercepts is because it illustrates the idea. When the function becomes harder, it is useful to understand the concepts. Going back to the basics is always a crucial to understanding something that seems complicated. Break it down and you will see it!! This is why mathematics can be so hard and so easy at the same time; once you grasp the concepts, it'll be easy, but if you don't, it will be difficult.