Lesson 4: Writing Equations in Two Variables

Property

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.
The independent variable is plotted along the horizontal axis, and the dependent variable is plotted along the vertical axis.

Examples

• Movie tickets cost 12 dollars each. If $c$ is the total cost and $t$ is the number of tickets, the equation is $c = 12t$. The number of tickets, $t$, is the independent variable.
• A bathtub has 20 gallons of water and drains at 4 gallons per minute. The amount of water $W$ after $m$ minutes is $W = 20 - 4m$. The minutes, $m$, is the independent variable.
• A phone's battery life $B$ starts at 100% and decreases by 10% each hour $h$. The equation is $B = 100 - 10h$. The hours, $h$, is the independent variable.

Explanation

An equation with two variables, like $c = 3p$, defines the relationship between two changing quantities. The independent variable is what you control (like pounds of apples), and the dependent variable is what you measure (the total cost).

Property

An ordered pair $(x, y)$ is a solution to a two-variable equation if substituting the $x$-value and $y$-value into the equation makes it true.

Examples

Property

Many real-world relationships can be expressed as two-variable equations using standard formulas: $d = rt$ (distance equals rate times time) and $P = 4s$ (perimeter of a square equals 4 times the side length).

Examples