Plane and solid analytic geometry, by William F. Osgood and William C. Graustein.

34

ANALYTIC GEOMETRY

The point of intersection of a line, for example,
(1) 2x- 3y + 4 = 0,
with the axis of x has its y-coordinate equal to 0. Consequently, to find the x-coordinate of the point, we have but to
set y = 0 in the equation of the line and solve for x. In this
case we have, then,
2x +4 = 0, or x=-2.
Similarly, the x-coordinate of the point of intersection of
the line with the axis of y is 0, and its y-co6rdinate is obtained
by setting x = 0 in the equation of the line and solving for y.
In the present case this gives
- 3y + 4 = 0, or y=-.
The points of intersection of the line (1) with the axes of
coordinates are, then, (- 2, 0) and (0, -). We now plot these
y points and draw the line through them.
043) We recognize the number 4 as the
intercept of the line (1) on the axis of y;
(-2,0) 0,x the number- 2 we call the intercept on
FIG. 5 the axis of x. We have plotted the line
(1), then, by finding its intercepts.
In general, the intercept of a line on the axis of a is the
x-coordinate of the point in which the line meets that axis. The
intercept on the axis of y is similarly defined. These definitions admit of extension to any curve. Thus, the circle of Ch. I,
~ 7, has two intercepts on the axis of x, namely, + 2 and - 2.
An axis or a line parallel to an axis has no intercept on that
axis. Every other line has definite intercepts on both axes,
and these intercepts determine the position of the line unless
they are both zero, that is, unless the line goes through the
origin.
EXERCISES
Determine the intercepts of the following lines on each of
the coordinate axes, so far as such intercepts exist, and draw
the lines.