By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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AG LOCI AND THEIR EQUATIONS. 44 44. Interval. On page 42, in studying the graph of the equation 9 x? + 25 '// = 225, we suggested considering the values of x in three sets of numbers: (1) from - oo to - 5, (2) from - 5 to 5, and (3) from 5 to oo. The set of all real numbers from one number a to a larger number b is called the interval from a to b. The notation a ~ x ~ b means that x is equal to or greater than a, and is equal to or less than b ; that is, it means that x may have any value in the interval from a to b, inclusive of a and b.

Variable and Constant. A quantity which is regarded as changing in value is called a variable~ A quantity which is regarded as fixed in value is called a constant. Frequently a symbol such as a, used to represent a constant, is free to represent any constant whatever, in which case it is called an arbitrm·y constant. For example, the equation (x- a) 2 + (y- /1) 2 = 1·2 represents a circle (§ 36) with any center (a, b) and any radius 1·, and so we speak of a, b, and 1·· as arbitrary constants and of x and y as variables.

8. (-1,- 2) and(- 2,- 4). 9. (a, b) and (c, d). 10. Find the equation of the line which passes through l A (3, - 2) and has the slope The condition under which P(x, y) moves is that the slope of AP is~- Find the equations of the lines through the following points and parallel to the x axis : 11. (4, -2). 12. (4, 7). ' 13. (a, 0). · 14. (-a, -b). Find the equations qf the lines through the following points and parallel to the y axis : , 15. (2, -1). -. 16. (6, 6). 17. (0, m). · 19. The equation of the x axis is y 18.

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