7th Grade Math: Help Using Graphs

Using Graphs in 7th Grade

By the time you're in 7th grade, you've probably mastered graphing skills, like plotting points. Now, you'll learn to use graphs to analyze and interpret real-world information. For instance, you might be asked to identify the unit rate in a graph or depict the solution to a word problem as an inequality.

Recognizing Proportional Relationships

One way that you can use graphs is to test for proportional relationships, where one variable changes by a constant number of units for every single-unit change in the other variable. If the line representing the relationship between the two variables is straight (linear), then there is a proportional relationship; if not, then the relationship isn't proportional.

As an example, imagine that the x values on a graph represent the distance traveled by a car, and the y values represent the amount of time that the car has been traveling. If the value of x increases by a set number of kilometers for every hour that passes, this means that the car is moving at constant rate. The line representing this relationship on a graph would be straight, and the relationship between the variables would be proportional.

Identifying Unit Rates

You can also use graphs to identify unit rates, like miles per hour or cost per item. To do this, draw a graph of your data. Then, observe the amount that the variable on the y axis (vertical axis) increases for every unit that the variable on the x axis (horizontal axis) increases. For instance, if the distance traveled is represented on the y axis, and it increases by 50 miles for every one hour shown on the x axis, then the unit rate would be 50 miles per hour.

Graphing Inequalities

You've probably already learned to graph lines, but now you can also use graphs to represent inequalities. To visualize this, start by imagining how you would graph the line x = y. It would pass through coordinates like (1, 1), (3, 3) and (-5, -5), forming a straight diagonal line through the origin (0, 0).

Now, imagine that instead of the equation x = y, you want to graph the inequality x > y. This inequality states that, instead of just being a single point, the value of x includes every point that's greater than the value of y. To graph this, draw the regular x = y line, and then shade in the area above the line. For the equation x < y, you would draw the x = y line, and then shade in all of the values below the line.