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Home Real and Hyperreal Numbers Straight Lines Definition
 
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Definition

DEFINITION

Let P(x0, y0) be a point and let m be a real number. The line through P with slope m is the set of all points Q(x, y) with

y - y0 = m(x - x0).

This equation is called the point-slope equation of the line (See Figure 1.3.1.)

The vertical line through P is the set of all points Q(x, y) with x = x0. Vertical lines do not have slopes.

01_real_and_hyperreal_numbers-62.gif

Figure 1.3.1

The slope is a measure of the direction of the line. Figure 1.3.2 shows lines with zero, positive, and negative slopes.

01_real_and_hyperreal_numbers-63.gif

Figure 1.3.2

The line that crosses the y-axis at the point (0, b) and has slope m has the simple equation.

y = mx + b.

This is called the slope-intercept equation for the line. We can get it from the point-slope equation by setting x0 = 0 and y0 = b.
Home Real and Hyperreal Numbers Straight Lines Definition

Last Update: 2006-11-15