Page:Elementary algebra (1896).djvu/499

610. The abscissa and ordinate of a point are called the co-ordinates of that point, and the lines XX' and YY' are called Co-ordinate Axes, Axis of X, and Axis of Y, or Axis of Abscissas, and Axis of Ordinates.

611. Any point in the plane can be given by means of these co-ordinates: thus the point P of Fig. 1 is located by measuring the distance a to the right of O on the axis of abscissas, and then taking a distance b vertically upwards.

Since a and b can be either positive or negative, a point P' is found by taking a positive and 6 negative; $P''$ is found by taking a negative and b negative; and $P'''$ is found by taking a negative and b positive.

Abscissas and ordinates are generally represented by x and y respectively. Thus for the point P, x =a, and y=b; for P', x=a, and y = -b, etc.

612. Instead of writing “the point whose co-ordinates are 5 and 3,” a more concise form is used: thus the point (5, 3) means that the point will be found by taking an abscissa of 5 units and an ordinate of 3.

Locate the points (3, - 2); (5, 8); (-4, 4): (- 8, -3).

GRAPH OF A FUNCTION.

613. Let $f(x)$ be any rational integral function of a, and let us place it equal to y. If we give a series of numerical values to x we can obtain corresponding values for y. Now laying off the values of x as abscissas, and the corresponding values of y as ordinates, we have a series of points which he upon a line called the graph of the given function.