Glossary for Lesson 6-1: Slope and Equations

y-Intercept

A y-intercept of a graph is a point at which the line or curve intersects the y-axis.  In this course, y-intercepts are defined as points, so we denote them as a coordinate pair, (0,b), where b is the y-coordinate of the y-intercept. The x-coordinate of any y-intercept will always be 0, since it must lie on the y-axis, which is the line x=0.  Because of this, some resources let the y-intercept refer to just the y-coordinate or the point, b in this case.

x-Intercept

An x-intercept of a graph is a point at which the line or curve intersects the x-axis.  In this course, x-intercepts are defined as points, so we denote them as a coordinate pair, (a,0), where a is the x-coordinate of the x-intercept.  The y-coordinate of any x-intercept will always be 0, since it must lie on the x-axis, which is the line y=0.  Because of this, some resources let the x-intercept refer to just the x-coordinate or the point, a in this case.

Slope-Intercept Form for the Equation of a Line

One way to write the equation of a line is to use slope-intercept form.  If we call the slope of a line m and the y-coordinate of its y-intercept b, then the equation of that line in slope-intercept form will be y=mx+b.

Perpendicular Lines

Two lines are called perpendicular if they form a 90^{\circ} angle.  This will happen if their slopes are the negative reciprocals of one another.  Put more mathematically, if a line has a slope of m, then every line perpendicular to it will have a slope of -\frac {1}{m}