Represent relationships using equations

A relationship between two quantities is represented by an equation by defining variables and expressing how one quantity depends on the other, using forms such as $y=kx$ for proportional relationships and $y=mx+b$ when a constant rate and an initial value are present. The equation should agree with a verbal description, table, or graph; the coefficient represents the rate of change and the constant represents the starting amount, without extending to systems, nonlinear relationships, or more advanced function notation.

Detailed Explanation: Represent relationships using equations

An equation shows how one quantity depends on another.

Choose variables.
Let $x$ be the number of hours a bike is rented.
Let $y$ be the total cost in dollars.
Find the rate of change.
The bike costs 3 $for each hour, so the cost increases by$ 3 $when$ x $increases by$ 1 $. This gives the term$ (3x)$.
Find the starting amount.
There is a 5 $starting fee, even when the bike is rented for$ 0 $hours. This is the constant$ 5$.
Write the equation.

y=3x+5

This equation means: multiply the number of hours by $3$ , then add the starting fee of $5$ .

Check the equation: If the bike is rented for $4$ hours, substitute $(x=4)$ :

y=3(4)+5=12+5=17

The total cost is 17 $, which agrees with the description. Here,$ 3 $is the rate of change, and$ 5$ is the initial value.

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Represent relationships using equations

Detailed Explanation: Represent relationships using equations

Learn by doing: Represent relationships using equations

Practice with unlimited practice problems

Practice:

Slope - Find Equivalent - X,Y Chart to Slope Zero Intercept Form