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

You will use linear functions to study real-world problems. Sales The number of computers sold per year since 2001 by T.J.'s Computers is given by the linear function $n(t)=25 t+350 .$ Here, $t$ is the number of years since 2001 (a) How many computers were sold in $2005 ?$ (b) What is the $y$ -intercept of this function, and what does it represent? (c) According to the function, in what year will 600 computers be sold?

You will use linear functions to study real-world problems.
Sales The number of computers sold per year since 2001 by T.J.'s Computers is given by the linear function $n(t)=25 t+350 .$ Here, $t$ is the number of years since 2001
(a) How many computers were sold in $2005 ?$
(b) What is the $y$ -intercept of this function, and what does it represent?
(c) According to the function, in what year will 600 computers be sold?

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Key Concepts

Linear Functions

Linear functions are mathematical expressions of the form y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (initial value). They are widely used to model situations with a constant rate of change, making them ideal for real-world problems like forecasting sales, budgeting, or measuring growth over time.

Slope (Rate of Change)

The slope in a linear function indicates how much the dependent variable (y) changes for each unit increase in the independent variable (x). In practical situations, it quantifies the constant rate at which something, such as sales or production, increases or decreases over time.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, corresponding to the value of the dependent variable when the independent variable is zero. It often represents an initial condition or starting value in many models, such as the initial quantity or baseline measurement in a real-world context.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that satisfies the given equation. In applied problems, this might mean determining the time at which a certain threshold is reached or finding an unknown quantity, both of which are critical skills for using linear functions in practical scenarios.

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