Writing Linear Equations & Expressions from Word Problems

Front

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.

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation 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 unit change in x.

Front

What is a constant in a linear equation?

Back

A constant in a linear equation is a fixed value that does not change. In the equation y = mx + b, the constant is represented by b, which is the y-intercept.

Front

How do you identify the rate in a word problem?

Back

The rate in a word problem is typically the amount of change per unit of time or per unit of another variable. It can often be found by analyzing how one quantity changes in relation to another.

Front

What is the difference between a fixed fee and a variable fee in word problems?

Back

A fixed fee is a one-time charge that does not change, while a variable fee changes based on usage or time, often represented as a rate multiplied by a variable.

Front

How can you represent a word problem with a linear expression?

Back

To represent a word problem with a linear expression, identify the fixed costs (constants) and the variable costs (rates), then combine them into an expression using a variable to represent the changing quantity.

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is equal to zero, represented by 'b' in the equation y = mx + b.

Front

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

Back

To convert a word problem into a linear equation, identify the quantities involved, determine the relationships between them, and express these relationships mathematically using variables.

Front

What is the significance of the startup fee in a word problem?

Back

The startup fee is a fixed cost that represents an initial payment required before any variable costs are incurred. It is often represented as a constant in a linear expression.