##### 9.2 Understanding tables of values of linear relationships

Linear Relations is basically looking at a graph and seeing a straight line traversing the x axis and the y axis diagonally as it is showing that all the values for x and y show a direct proportion with each other. This simply means that if you look at the table of values, as the value of x increases or decreases, so as the value of y. If you are not seeing a straight line in your grid paper, then it means it does not represent a linear relationship.

In 9.1 we will see that Linear Relations can tell us patterns like whether or not a business is making profits, or if products are sold at a successful rate. We will learn how to understand a given graph and look at the relation of the given values. By looking at the line we can be able to deduce conclusions like it the graph is going up, then the values of x and y are increasing and it is going down then their values are decreasing.

In 9.2 we will be able to understand linear relationships by just looking at the table of values provided. We will learn how to spot table of values that represent a linear relationship and which don’t show such. Using the table of value given we will also be learning how to graph the values to illustrate the linear relationship that it has. You may do this manually or you can just use a free graphing tool online.

9.3 will teach us the application of Linear Relationships. We are going to learn how to solve math problems involving linear relations like solving for y. Here in this part of the chapter, we can be able see that linear relationships only have two variables in their equations, like in speed, you only have distance and time. In computing for sales you only have the price of a product and the number of items solved. In computing for how much you need to pay for given pieces of chocolates sold at a certain price you also have two variables, the number of pieces and the amount of money you will spend according to the number of pieces you need. Even the global warming issue shows the same kind of relationship. Scientists found that carbon dioxide emissions and global warming is in a linear relationship.

In no time, you would be ready to solve linear relations problem and be able to understand the next chapter which is very much related to this chapter.

### Understanding tables of values of linear relationships

Linear equations represent direct proportional relationships between x and y. A table of values contains the exact values of x and y. In this section, we will learn how to draw graphs based on the data from tables of values. From the tables and graphs, we will try to describe and determine whether the relationships are linear or not.