Honors Geometry Section 3.8 Lines in the Coordinate Plane.

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Presentation transcript:

Honors Geometry Section 3.8 Lines in the Coordinate Plane

Objectives: 1. Find the slope of the line through 2 points. 2. Find the slope of a line parallel to a given line. 3. Find the slope of a line perpendicular to a given line. 4. Write the equation of a line.

The slope of a line is a ratio that indicates how a line rises or falls from left to right.

The slope of a nonvertical line that contains the points is equal to the ratio

When graphing, it is helpful to think of slope as rise over run.

What would the slope of a vertical line be? Why?

Examples: Find the slope of the line through the given points.

Two nonvertical lines are parallel iff their slopes are equal. Note: Vertical lines will be parallel.

Two nonvertical lines are perpendicular iff their slopes are opposite reciprocals. Note: A horizontal line and a vertical line are perpendicular. change the sign flip the fraction

There are two forms for an equation of a line with which you should be familiar. Slope-intercept form: Point-slope form:

Example: Write an equation in point-slope form for the line through the point (3, -5) with a slope of.

Example: Write an equation, in slope- intercept form, for the line through the point (12, 5) that will be perpendicular to the line.

Example: Write an equation, in slope- intercept form, for the line through the points (2, -5) and (4, 2).