Use the given conditions to write an equation for each line in point-slope form and general form

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Use the given conditions to write an equation for each line...

Key Concepts

Point-Slope Form

The point-slope form of a line is an equation that expresses a line given its slope and a point on the line. It is typically written as y - y? = m(x - x?), where (x?, y?) is a known point on the line and m is the slope. This form is particularly useful when you know one point and the slope of the line, allowing for immediate formulation of the line's equation.

General Form of a Line

The general form of a line is an equation expressed as Ax + By + C = 0, where A, B, and C are constants. This form is useful because it provides a standardized way to represent lines, making it easier to compare and analyze them, especially when working with systems of equations or performing algebraic manipulations.

Slope Calculation

The slope of a line is a measure of its steepness and direction, defined as the ratio of the change in y to the change in x between any two points on the line. It is a fundamental concept for defining linear relationships and plays a crucial role in various forms of a line's equation.

Perpendicular Lines

Two lines are perpendicular if they intersect at a right angle (90 degrees). In the context of linear equations, this means the slopes of the two lines are negative reciprocals of each other. This relationship allows for the determination of the slope of a line that is perpendicular to a given line, using the known slope of the original line.

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