Mathematics
Grade 10
15 min
Complete a table for a two-variable relationship
Complete a table for a two-variable relationship
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1
Introduction & Learning Objectives
Learning Objectives
Identify the independent and dependent variables in a given two-variable equation.
Substitute given values for an independent variable into linear and quadratic equations.
Solve for the corresponding dependent variable using the correct order of operations.
Accurately record the resulting ordered pairs (x, y) in a table of values.
Complete a table of values for linear, quadratic, and other simple polynomial relationships.
Use a completed table to identify patterns and check for consistency in a relationship.
Interpret the meaning of a completed ordered pair in the context of a real-world problem.
Ever wondered how a GPS calculates your arrival time based on your speed? 🚗 That's a two-variable relationship in action!
This tutorial revisits a funda...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, typically a letter (like x or y), that represents a quantity that can change or take on different values.In the equation `d = 60t`, `d` (distance) and `t` (time) are variables.
Two-Variable RelationshipAn equation or rule that connects two variables, showing how the value of one variable depends on the value of the other.The equation `y = 2x + 3` defines a relationship where the value of `y` is always 3 more than twice the value of `x`.
Independent VariableThe variable (often `x`) that is changed or manipulated in an equation. It is the 'input' value.In `y = x^2 - 4`, you choose a value for `x` to calculate `y`. Therefore, `x` is the independent variable.
Dependent VariableThe variable (often `y`) whose value is determined by the independe...
3
Core Formulas
Substitution Principle
Given an equation `y = f(x)` and a value `x = a`, substitute `a` for every instance of `x` to find the corresponding value of `y`.
This is the core action for completing a table. You take the given 'input' value and place it into the equation to find the 'output'.
Order of Operations (PEMDAS)
P (Parentheses) → E (Exponents) → MD (Multiplication/Division from left to right) → AS (Addition/Subtraction from left to right)
After substituting, you must follow this strict order to simplify the expression correctly. Errors here are very common, especially with exponents and negative numbers.
Linear Equation Form
y = mx + b
Recognizing this form tells you the relationship is linear. The `y` values in your table should increase or de...
4 more steps in this tutorial
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Challenging
A table shows a two-variable relationship. Given the ordered pairs (0, 2), (1, 3), (2, 6), and (3, 11), what is the y-value when x = 4?
A.15
B.18
C.20
D.16
Challenging
To complete a table of values for the equation 3x + y = 8, you first need to express it in a form that isolates the dependent variable y. Once rearranged, what is the value of y when x = -2?
A.2
B.10
C.-14
D.14
Challenging
The cost C to rent a hall is C = 20n + 100, where n is the number of guests. The table includes the point (50, 1100). What is the cost for 70 guests, and what does the point (50, 1100) mean?
A.Cost is $1500; it means 1100 guests cost $50.
B.Cost is $1400; it means 50 guests cost $1100.
C.Cost is $1500; it means 50 guests cost $1100.
D.Cost is $1400; it means the maximum cost is $1100 for 50 guests.
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