Lesson 3: Solve Problems Using Ordered Pairs

Property

To graph the relationship shown in a table, treat each row as an ordered pair $(x, y)$. The first column is the x-coordinate, and the second column is the y-coordinate. Plot each ordered pair as a point on the coordinate plane.

Examples

• Given the table:

The points to graph are $(1, 3)$, $(2, 6)$, and $(3, 9)$.

• Given the table:

The points to graph are $(0, 0)$, $(1, 15)$, and $(2, 30)$.

Explanation

A table of values is a way to organize the relationship between two variables. Each row in the table corresponds to a specific point on a graph. To plot these points, you use the value from the first column as the x-coordinate and the value from the second column as the y-coordinate. This process transforms the data from the table into a visual representation on the coordinate plane.

Property

Real-world problems involving two related quantities, $x$ and $y$, can be solved by graphing. The relationship is represented by a set of ordered pairs $(x, y)$, which are plotted on a coordinate plane. The resulting graph can be used to find unknown values by extending the pattern.

Examples

• A food truck sells tacos for 3 dollars each. The relationship between the number of tacos bought ($x$) and the total cost ($y$) can be graphed. Using the graph, you can find the cost of 5 tacos by finding the $y$-value when $x=5$. The point $(5, 15)$ on the graph shows the cost is 15 dollars.
• A plant is 5 cm tall and grows 2 cm each week. Graph the relationship between the number of weeks ($x$) and the plant''s height ($y$). To find the plant''s height after 4 weeks, locate $x=4$ on the graph and find the corresponding $y$-value, which would be at the point $(4, 13)$.

Explanation

This skill involves translating a word problem into a visual graph to find a solution. First, identify the two quantities that change and assign them to the $x$- and $y$-axes. Then, create a table of values based on the rule in the problem and plot these ordered pairs as points. Finally, use the pattern of the points on the graph to find the answer to the question asked in the problem.