linear equations

What is a linear equation?

An algebraic equation in which each term is either a constant or the product of a constant and a single variable, which results in a straight line when graphed on a coordinate plane.

What is the slope-intercept form of a linear equation?

The form y = mx + b, where m represents the slope and b represents the y-intercept.

What is the standard form of a linear equation?

The form Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

What is the point-slope form of a linear equation?

The form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line.

How is the slope (m) calculated between two points (x1, y1) and (x2, y2)?

The slope is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}, often referred to as 'rise over run'.

What is a y-intercept?

The point where the graph of the equation crosses the y-axis, occurring where x = 0.

What defines a horizontal line in a linear equation?

A line with a slope of 0, represented by the equation y = c, where c is a constant.

What defines a vertical line in a linear equation?

A line with an undefined slope, represented by the equation x = c, where c is a constant.