Analytic Geometry by Gordon Fuller, Dalton Tarwater

By Gordon Fuller, Dalton Tarwater

Tailored for a primary path within the research of analytic geometry, the textual content emphasizes the basic components of the topic and stresses the ideas wanted in calculus. This re-creation was once revised to provide the topic in a latest, up to date demeanour. colour is used to spotlight options. know-how is built-in with the textual content, with references to the Calculus Explorer and advice for utilizing graphing calculators. a number of new themes, together with curve becoming related to mathematical modeling have been further. workouts have been up-to-date. New and sundry purposes from drugs to navigation to public overall healthiness have been added.

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3y by equa- 4 = - 10 + 3z/ + 3* + 3y = 6 0. = 0. = 0. 1. In each problem 25-36, write the equation of the line determined by the slope m and the ^-intercept 6. 25. m = 3; b = -4. 27. m = -4; b = 5. 29. m = 6 - -2. = 31. m 0; 6 = -6. 33. m = -J; 6 = -8. 35. m = 0; b = 0. ; 26. 28. 30. 32. 34. 36. = 2; 6 = 3. = -1;6 = 1. = $ 6 = -6. -5; 6 = 0. = 0; b = -2. m = - 6 = 0. m m m m m ; ; THE STRAIGHT LINE 36 Write the equation of the problem 37-48. line [CHAP. 3 which has the ^-intercept a and the ^-intercept 6 in each 37.

Solving for y gives, where B 7* 0, equation A we have seen, is the slope of the line. By setting notice that the constant term is the ^-intercept. Substituting for the slope and b for the ^-intercept, we obtain the simpler form The x m C coefficient of x, as we 0, y This is called the slope-intercept tion in this form which it SB mx + form makes evident the b. (2) of the equation of a line. slope and the y-intercept An equa- of the line Conversely, the equation of a line of given slope and be written at once by substituting the proper values for represents.

Written in the form 7^2 = > mi which expresses one slope as the negative reciprocal of the other Two THEOREM. of one is the EXAMPLE. 4 (-2,3), slant lines are perpendicular if, and only negative reciprocal of the slope of the other. if, slope. the slope Find the tangents of the angles of the triangle whose vertices are Find each angle to the nearest degree. (See #(8, -5), and C(5,4). ) Solution. formula (1), The slopes we get A( -2,3) of the sides are indicated in Fig. 2-11. C(5,4) 5(8, -5) FIGURE 2-11 Substituting in FUNDAMENTAL CONCEPTS AND FORMULAS 26 [CHAP.

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