You will use linear functions to study real-world problems....

You will use linear functions to study real-world problems. Sales The number of handbags sold per year since 2003 by Tres Chic Boutique is given by the linear function $h(t)=160 t+500 .$ Here, $t$ is the number of years since 2003 (a) How many handbags were sold in $2006 ?$ (b) What is the $y$ -intercept of this function and what does it represent? (c) According to the function, in what year will 1200 handbags be sold?

You will use linear functions to study real-world problems.
Sales The number of handbags sold per year since 2003 by Tres Chic Boutique is given by the linear function $h(t)=160 t+500 .$ Here, $t$ is the number of years since 2003
(a) How many handbags were sold in $2006 ?$
(b) What is the $y$ -intercept of this function and what does it represent?
(c) According to the function, in what year will 1200 handbags be sold?

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Key Concepts

Linear Functions

A linear function represents a relationship between two quantities where the rate of change is constant. It is typically written in the form f(x) = mx + b, where m is the constant rate of change (or slope) and b is the initial value (or y-intercept). This function is fundamental in modeling relationships in which changes occur uniformly over time or another variable.

Slope (Rate of Change)

The slope of a linear function indicates how much the dependent variable increases or decreases with a one-unit increase in the independent variable. It captures the rate at which the relationship changes and is essential for understanding trends and making predictions in various real-world contexts.

Y-intercept

The y-intercept is the point where the graph of a linear function crosses the y-axis, representing the value of the function when the independent variable is zero. This concept provides a starting point or initial condition for the scenario being modeled and is vital in interpreting linear relationships.

Solving Linear Equations

Solving linear equations involves substituting known values into the equation to find unknown variables. This technique is crucial in applying linear models to real-world problems, as it allows one to determine specific outcomes or time points based on the relationship defined by the function.

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