Understanding linear equations in one variable

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Front

How do you represent a ratio in an equation?

Back

A ratio can be represented in an equation by using variables. For example, if two numbers are in the ratio 5:7, you can represent them as 5x and 7x.

Front

What is the first step to solve a linear equation?

Back

The first step to solve a linear equation is to isolate the variable on one side of the equation.

Front

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

Back

Identify the quantities involved, assign variables to them, and translate the relationships and operations described in the problem into an equation.

Front

What does it mean to 'isolate the variable'?

Back

To isolate the variable means to manipulate the equation so that the variable is alone on one side of the equation.

Front

What is the solution to the equation 2a = 20?

Back

The solution is a = 10.

Front

How do you check if your solution to a linear equation is correct?

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

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

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.

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.

Front

How do you write an equation from a verbal statement?

Back

Identify the key quantities and operations in the statement, then translate them into mathematical symbols and variables.