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 the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the meaning of the term 'total cost' in a word problem?

Back

Total cost refers to the overall amount of money spent, which may include fixed fees and variable costs based on usage.

Front

How do you identify fixed and variable costs in a word problem?

Back

Fixed costs remain constant regardless of usage (e.g., deposit fees), while variable costs change based on the level of usage (e.g., cost per hour or per mile).

Front

What is the importance of defining variables in a word problem?

Back

Defining variables helps to clarify what each quantity represents, making it easier to formulate equations and solve the problem.

Front

How can you check if your linear equation is correct?

Back

You can check if your linear equation is correct by substituting values for the variables and verifying if the equation holds true.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values that satisfy all equations simultaneously.