Writing Equations for Linear Word Problems

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What is a linear equation?

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A linear equation is an equation that represents a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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How do you represent earnings in a linear equation?

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Earnings can be represented as a function of hours worked, typically in the form E = rate * h - costs, where 'rate' is the payment per hour, 'h' is the number of hours worked, and 'costs' are any fixed expenses.

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What is the formula to calculate total cost in a rental scenario?

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The total cost can be calculated using the formula C = fixed fee + (variable rate * quantity), where 'fixed fee' is a one-time charge, 'variable rate' is the cost per unit, and 'quantity' is the number of units used.

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How do you set up an equation for a budget constraint?

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To set up an equation for a budget constraint, you can use the formula total budget = (cost per item * number of items) + fixed costs.

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What does the slope represent in a linear equation related to costs?

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In a linear equation related to costs, the slope represents the variable cost per unit, indicating how much the total cost increases for each additional unit consumed.

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What is the significance of the y-intercept in a cost equation?

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The y-intercept in a cost equation represents the fixed costs that are incurred regardless of the quantity produced or consumed.

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How can you determine the maximum quantity of items you can purchase within a budget?

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To determine the maximum quantity of items you can purchase within a budget, set up the equation based on the total cost and solve for the quantity, ensuring the total cost does not exceed the budget.

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What is the relationship between total cost and miles driven in a rental scenario?

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The relationship can be expressed as a linear equation where total cost = fixed rental fee + (cost per mile * miles driven).

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How do you convert a cost equation into a standard form?

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To convert a cost equation into standard form, rearrange the equation to isolate the variable terms on one side and the constant on the other, typically in the form Ax + By = C.

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What is the role of constants in linear equations?

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Constants in linear equations represent fixed values that do not change with the variable, such as initial costs or fees.