Writing Linear Equations from Word Problems

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What is a linear equation?

Back

A linear equation is an equation that models a relationship between two variables in which the highest power of the variable is one. 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 determine the slope in a linear equation from a word problem?

Back

The slope represents the rate of change in the context of the problem. It can be determined by identifying how much one quantity changes in relation to another quantity.

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What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the initial value of the dependent variable when the independent variable is zero.

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How can you write a linear equation from a word problem involving a decreasing quantity?

Back

Identify the initial value and the rate of decrease. The equation will typically be in the form y = -mx + b, where m is the rate of decrease.

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What is the formula to calculate the remaining amount after a certain number of withdrawals?

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The formula is y = initial amount - (withdrawal amount * number of withdrawals).

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How do you find the total amount after a certain number of deposits?

Back

The formula is y = initial amount + (deposit amount * number of deposits).

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What is the significance of the negative sign in a linear equation representing a decrease?

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The negative sign indicates that the quantity is decreasing over time, reflecting a loss or withdrawal.

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How can you interpret the slope of a linear equation in a real-world context?

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The slope indicates the rate of change, such as how fast something is increasing or decreasing, which can be interpreted in terms of time, money, distance, etc.

Front

What is the first step in solving a word problem that requires writing a linear equation?

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Identify the variables involved and what they represent in the context of the problem.

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How do you convert a word problem into a linear equation?

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Extract key information such as initial values, rates of change, and relationships between variables, then express this information in the form of a linear equation.