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

Front

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

Back

Identify the variables, determine the relationships between them, and translate the relationships into an 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 difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled in an experiment, while the dependent variable is the one that is measured or affected.

Front

How can you determine the number of solutions to a system of linear equations?

Back

A system of linear equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines).

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical problem that is presented in the form of a narrative or real-life scenario, requiring interpretation and translation into mathematical expressions.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the numerical factors that multiply the variables in the equation, indicating their contribution to the equation's value.