Multistep Equations and INequalities

Front

What is a multistep equation?

Back

A multistep equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

How do you determine if an equation has one solution, no solutions, or infinitely many solutions?

Back

You can determine this by simplifying the equation. If you end up with a true statement (like 0=0), it has infinitely many solutions. If you get a false statement (like 0=5), it has no solutions. If you find a specific value for the variable, it has one solution.

Front

What does it mean for two lines to be the same in a system of equations?

Back

It means that the two equations represent the same line on a graph, resulting in infinitely many solutions.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no rise as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run (change in x) is 0.

Front

How can you tell if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.