P=1.5 t-300 represents the profit in dollars from selling t...

$P=1.5 t-300$ represents the profit in dollars from selling $t$ printed T-shirts.
a. Find the profit if you sell 100 printed T-shirts.
b. Find the profit if you sell 400 printed T-shirts.
c. How many printed T-shirts must you sell to make $\$ 1000$ in profit?

Key Concepts

Solving Linear Equations

Solving linear equations involves isolating the unknown variable to determine its value under certain conditions. This is crucial in profit analysis when determining how many units must be sold to reach a desired profit level.

Substitution Method

Substitution is a method used to evaluate functions by replacing the variable with specific values. This process is essential for determining the outcome or profit when a given number of units are sold.

Slope

The slope is a key component of a linear equation that represents the rate at which the dependent variable changes in relation to the independent variable. In economic models, this value indicates how much profit increases or decreases for each additional unit sold.

Linear Functions

A linear function represents a relationship where there is a constant rate of change between two variables. In many real-world contexts, such as business, the relationship between the number of items sold and the profit can be described by a linear function, with the slope indicating the change in profit per unit sold and the intercept representing fixed costs or starting conditions.

Y-intercept

The y-intercept is the constant term in a linear equation, signifying the value of the dependent variable when the independent variable is zero. In business applications, it often reflects fixed costs or the initial state before any goods are sold.

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