Writing Linear Equations 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 it mean to write a linear equation from a word problem?

Back

Writing a linear equation from a word problem involves translating the situation described in the problem into a mathematical equation that can be solved.

Front

In the equation 222.5 = 35 + 0.75m, what does each term represent?

Back

222.5 represents the total rental charge, 35 is the fixed cost of renting the car, and 0.75m represents the variable cost based on miles driven.

Front

How do you identify variables in a word problem?

Back

Variables are typically quantities that can change or vary. Look for words that indicate amounts, such as 'number of miles', 'total cost', or 'hours rented'.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

Front

How do you determine the fixed cost in a word problem?

Back

The fixed cost is the amount that does not change regardless of the quantity used or purchased. It is often stated as a flat fee.

Front

What does the term 'function' mean in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

Front

In the function S(d) = 3h + 0.90d, what does each variable represent?

Back

S(d) represents the total salary, h is the number of hours worked, and d is the amount of tips received.

Front

What is the importance of identifying the dependent and independent variables?

Back

Identifying dependent and independent variables helps in understanding how one variable affects another and is crucial for writing accurate equations.

Front

How can you represent a relationship between two quantities in a word problem?

Back

You can represent a relationship by forming an equation that connects the two quantities, often using variables to denote each quantity.