Writing Equations for Linear Word Problems

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What is a linear equation?

Back

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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How do you represent earnings in a linear equation?

Back

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

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?

Back

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

Tags

CCSS.HSA.CED.A.3

Front

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

Back

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.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

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.

Tags

CCSS.6.EE.B.7

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

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.

Front

What is the role of constants in linear equations?

Back

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

Tags

CCSS.HSF.LE.B.5