Equation of a line

The value of $y$ when $x=0$ , if it exists, is called the $y$ -intercept. Geometrically, if $d$ is the $y$ -intercept, then $(0,d)$ is the point of intersection of the line and the $y$ -axis. The $y$ -intercept exists iff the line is not parallel to the $y$ -axis. The $x$ -intercept is defined similarly.

If $b\neq0$ , then the above equation of the line can be rewritten as $$ y = mx + d. $$ This is called the slope-intercept form of a line, because both the slope and the $y$ -intercept are easily identifiable in the equation. The slope is $m$ and the $y$ -intercept is $d$ .

Three finite points $(x_1,\,y_1)$ , $(x_2,\,y_2)$ , $(x_3,\,y_3)$ in are collinear if and only if the following determinant vanishes:

Line segment

Let $p_1 = (x_1,\,y_1)$ and $p_2 = (x_2,\,y_2)$ be distinct points in . The closed line segement generated by these points is the set