Linear equations (two variables)

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

What does the solution of a linear equation represent?

Back

The solution of a linear equation represents the point (x, y) where the line intersects the coordinate plane.

Front

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

Back

A system of linear equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinite solutions?

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 graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on the coordinate plane.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line given two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept of a linear equation is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the x-intercept of a linear equation?

Back

The x-intercept of a linear equation is the point where the line crosses the x-axis, represented as (a, 0) in the equation y = mx + b.

Front

How can you tell if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

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.