Graph a two-variable relationship

Learning Objectives Define a two-variable relationship and identify its components. Create a table of values by applying a given rule to input numbers. Form ordered pairs from a table of values. Accurately plot ordered pairs on a coordinate plane. Identify and describe simple patterns observed in graphed points. Understand how a graph visually represents a two-variable relationship. Have you ever noticed how the number of cookies you bake changes with the amount of flour you use? 🍪 Or how the total cost of pencils depends on how many you buy? 🤔 In this lesson, we'll learn how to show these kinds of changing relationships using graphs! You've learned about variables and coordinate planes. Now, we'll put them together to explore how two variables can be relat...

TermDefinitionExample VariableA letter or symbol (like 'x' or 'y') that represents a number that can change or vary.In the rule `y = x + 3`, 'x' and 'y' are variables. Two-Variable RelationshipA connection between two variables where a change in one variable affects the other, often described by a rule.If you buy 'x' apples and each costs $1, the total cost 'y' is related by `y = x`. Rule (or Equation)A mathematical statement that describes how two variables are related.`y = x + 5` is a rule where 'y' is always 5 more than 'x'. Table of ValuesAn organized list that shows pairs of numbers that satisfy a given rule for a two-variable relationship.For `y = x + 1`, a table might show (x=1, y=2), (x=2, y=3). Ordere...

Rule for Creating a Table of Values To create a table of values from a rule like `y = x + A` or `y = x \times A`, choose several input values for `x`, substitute each into the rule, and calculate the corresponding output value for `y`. This rule helps you find specific pairs of numbers that fit the relationship. You pick easy numbers for 'x' (like 0, 1, 2, 3) and use the rule to find 'y'. Rule for Forming Ordered Pairs Each row in your table of values represents an ordered pair `(x, y)`, where `x` is the input value and `y` is the calculated output value. Once you have your 'x' and 'y' values from the table, you write them as `(x, y)` to prepare them for plotting on the coordinate plane. Rule for Plotting Ordered Pairs To plot an...