What are the characteristics of Lines in the Plane?

Section P4 (new text)

Slope

• The slope of the nonvertical line through the points (x1, y1) and (x2, y2) is

• If the line is vertical, then x1 = x2 and the slope is undefined.

ExampleFind the slope of the line between these points.

Point-Slope Form

• The point-slope form of an equation of a line that passes through the point (x1, y1) and has the slope m is

ExampleUse Point-Slope form to find an equation of the line that passes through the following point with the given slope. Put your answer in Slope-Intercept form.

Slope-Intercept Form

• The slope-intercept form of an equation of a line with slope m and y-intercept (0, b) is

General & Standard Form

• General Form (A and B not both zero)

• Standard Form (A and B not both zero)

Intercepts

• X-intercept—

• Y-intercept—

• You can find the intercepts and use them to graph the line.

Where the line crosses the x-axis (y = 0)

Where the line crosses the y-axis (x = 0)

Parallel and Perpendicular Lines

• Parallel lines have equal slopes.

• Perpendicular lines have opposite, reciprocal slopes