Flashcard 6: System of linear equations

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, y).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the zero of a function?

Back

The zero of a function is the x-value where the function equals zero, also known as the x-intercept.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, indicating that the system of equations has no solution.

Front

What does it mean if two lines intersect?

Back

If two lines intersect, it means they have one solution, which is the point of intersection.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Front

How can you tell if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and do not intersect.

Front

What is the graphical representation of a system with one solution?

Back

The graphical representation is two intersecting lines.

Front

What happens when you graph the same equation twice?

Back

You will graph the same line, resulting in infinitely many solutions.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are constants.