6.1 Representing patterns in linear relations

From a previous chapter on linear relations, we learned that Linear Relations are basically relationships that show a graph with a straight line traversing the x axis and the y axis diagonally. This relationship illustrates that as the value of x increases or decreases, the value of y increases or decreases too. We also learned that if you are not seeing a straight line in your grid paper, then it means it’s not a linear relationship.

In the chapter on linear equations, we learned all about linear equations and their table of value. In this chapter however, instead of just looking at a certain graph that’s made from a table of values, we would be learning how to represent patterns into a linear relation. In 6.1 we have activities that would use shapes and other figures to illustrate linear relation.

In 6.2, not only do we rely into looking at the table of values to know the value of a certain variable but also we would learn how to look at the graph so we could solve for the value of a particular variable. This is done by using the graph to deduce the equation. The equation is consisted of variables, numerical coefficient, and the constant. So if we have y = 3x + 4, 3 is the numerical coefficient, x and y are the variables and 4 is the constant. There are series of values in just a single line graph and not all of these are listed in the table of values so with 6.2 we would be able to strengthen our ability to read graphs. To check your graph and the values of your x and y, you can go to an online graphing calculator.

Finally, in 6.3 we will learn how to solve word problems by graphing the equation given. From our previous discussion on linear equations, we know that the general formula is y = mx + b where m is the slope, and b is the y intercept. We are to use that to interpolate the values that would be found in the line and to extrapolate on the trend if ever needed in order to solve the problem.

Representing patterns in linear relations

In this section, we will learn how to represent patterns in linear relations. In other words, these patterns will form a straight line if they are plotted on a graph paper. We can start with creating a table of values which has the independent variable as X, and dependent variable as Y. One way to represent patterns in linear relations is to use the slope-intercept form.


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  • 2.
    Two identical octagons are attached to each other. All the sides in each octagon have the same length.

  • 3.
    Write the linear equation that represents the relationship of each set of numbers.
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Representing patterns in linear relations

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