Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is and the direction it is going.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does it mean to have infinite solutions in a system of linear equations?

Back

A system of linear equations has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.