Identify the initial value of a linear relationship

The initial value of a linear relationship is the dependent-variable value when the independent variable is zero; it is the y-intercept and the constant $b$ in an equation such as $y=mx+b$ . It can be identified from a table, graph, equation, or context and distinguished from the rate of change, providing the starting amount for interpreting and constructing linear models.

Detailed Explanation: Identify the initial value of a linear relationship

The initial value is the value of the dependent variable, $y$ , when the independent variable, $x$ , is $0$ . In an equation of the form

y=mx+b,

the initial value is $b$ , the constant term. It is also the $y$ -intercept.

Example: A taxi fare is modeled by

C=2.50m+4,

where $m$ is the number of miles traveled and $C$ is the cost in dollars.

Identify the independent variable: $m$ , the miles traveled.
Identify the dependent variable: $C$ , the cost.
Look for the value of $C$ when $m=0$ :

C=2.50(0)+4

C=4

Therefore, the initial value is $\boxed{4}$ dollars.

This means the taxi costs 4 $before any miles are traveled. The number$ 2.50$ is the rate of change, or the cost per mile, not the initial value.

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Y Intercept of a Line from Coordinates of Points and Slope

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Identify the initial value of a linear relationship

Detailed Explanation: Identify the initial value of a linear relationship

Learn by doing: Identify the initial value of a linear relationship

Practice with unlimited practice problems

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Y Intercept of a Line from Coordinates of Points and Slope