linear equation

Front

What is a linear equation?

Back

A linear equation is an equation that makes 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 (m) represent in a linear equation?

Back

The slope (m) 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 (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the y-intercept from a graph?

Back

To find the y-intercept from a graph, look for the point where the line intersects the y-axis.

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

How can you determine if two lines are parallel?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1 (i.e., m1 * m2 = -1).

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to calculate the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a linear equation has no solution?

Back

A linear equation has no solution if the lines are parallel and never intersect.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

A linear equation has infinitely many solutions if the lines are coincident, meaning they lie on top of each other.