Geometry: Parallel Lines and Slopes

Lines in the same plane that never intersect.

Parallel lines have equal slopes.

The point where a graph crosses the y-axis.

Steepness and direction of a line.

Where two lines cross.

Lines that intersect at a 90-degree angle.

Perpendicular lines have slopes that are negative reciprocals of each other.

A way to write a linear equation using the slope (m) and a point on the line ((x₁, y₁)). It is represented as y - y₁ = m(x - x₁).

A set of equations used to find the intersection point of two lines.

It's called point-slope form because it uses a point on the line and the slope to define the equation.

The variable m represents the slope of the line.

(x₁, y₁) represents a specific point that lies on the line.

1. Identify the slope (m) and a point ((x₁, y₁)). 2. Substitute the values directly into the Point-Slope Form equation: y - y₁ = m(x - x₁).

Given a slope of 3 and a point (2, 1), the Point-Slope Form equation would be: y - 1 = 3(x - 2).

If the slope m is 0, the Point-Slope Form equation simplifies to y - y₁ = 0(x - x₁). This results in y - y₁ = 0 which can be rewritten as y = y₁. This represents a horizontal line.

If the slope m is negative, the Point-Slope Form equation will contain a negative sign before the m in the formula: y - y₁ = -m(x - x₁).

The variables x and y are always present in linear equations, representing the horizontal (x) and vertical (y) coordinates on a graph.

A common error is forgetting the negative sign in front of the y₁ term when substituting a point with a negative y value. For example, y + (-5) = -2(x - 4) should be corrected to y - (-5) = -2(x - 4).

Point-slope form is used to write the equation of a line when you know its slope (m) and a point that lies on it (x1, y1).

In point-slope form, 'm' represents the slope of the line. It tells you how steep the line is and its direction.

(x1, y1) represents a specific point that lies on the line. It gives you a starting location on the line.

1. Identify the slope (m) and a point (x1, y1). 2. Substitute the values directly into the Point-Slope Form equation: y - y1 = m(x - x1).

If the slope 'm' is 0, the line is horizontal. The Point-Slope Form simplifies to y - y1 = 0, which is the same as y = y1.

If the slope 'm' is negative, the line goes downwards from left to right. The Point-Slope Form equation will have a negative sign before the 'm'.

The variables 'x' and 'y' are always present in linear equations. 'x' represents the horizontal coordinate, and 'y' represents the vertical coordinate.

It's called 'point-slope' form because it uses a specific point and the slope to define the equation of a line.

You can write the equation of a line using only the slope and a point on the line.

It takes the slope and a point on the line, and plugs those values into a formula to create the equation of that specific line.

It's a convenient way to write the equation of a line, especially when you know the slope and a point on the line.