Linear Models

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What is a linear model?

Back

A linear model is a mathematical representation of a relationship between two variables that can be expressed in the form of a linear equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

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What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the linear relationship on the y-axis.

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How do you find the total cost in a linear cost model?

Back

The total cost can be found using the equation c = mx + b, where m is the cost per unit, x is the number of units, and b is the fixed cost.

Front

What does the function f(n) = 12n + 500 represent?

Back

This function represents a linear relationship where the total amount given to charity increases by $12 for each additional student present, starting from a base amount of $500.

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How do you determine the number of students needed to reach a donation goal using a linear function?

Back

To find the number of students needed, set the function equal to the donation goal and solve for n.

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What is the significance of V(t) = 25000 - 3000t in the context of car value?

Back

This function represents the depreciation of a car's value over time, where V(t) is the value t years after purchase, starting from an initial value of $25,000 and decreasing by $3,000 each year.

Front

What does V(0) represent in the car value function?

Back

V(0) represents the purchase price of the car, as it indicates the value at the time of purchase.

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How do you write an equation for total cost based on variable costs?

Back

The equation can be written as c = variable cost per unit * number of units + fixed cost.

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What is the total cost if a driving range charges $4 to rent a golf club and $2.75 for each bucket of golf balls?

Back

The total cost can be expressed as c = 2.75b + 4, where b is the number of buckets.