By Samuel Moy

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The form x = a where a is 11 11 29. The equation of the horizontal line through 31. We have the points (1, 4) and (−2, 13). First we ﬁnd the slope. 13 − 4 9 m= = = −3 −2 − 1 −3 We will use the point-slope equation, choosing (1, 4) for the given point. y − 4 = −3(x − 1) y − 4 = −3x + 3 y = −3x + 7, or h(x) = −3x + 7 Then h(2) = −3 · 2 + 7 = −6 + 7 = 1. 33. We have the points (5, 1) and (−5, −3). First we ﬁnd the slope. −3 − 1 −4 2 m= = = −5 − 5 −10 5 We will use the slope-intercept equation, choosing (5, 1) for the given point.

B) No. The change in the outputs varies. c) No. Constant changes in inputs do not result in constant changes in outputs. Copyright © 2013 Pearson Education, Inc. 3 37 5. Two points on the line are (−4, −2) and (1, 4). y2 − y1 6 4 − (−2) m= = = x2 − x1 1 − (−4) 5 39. 7 is a horizontal line, so the slope is 0. 7). 7. Two points on the line are (0, 3) and (5, 0). −3 3 0−3 y2 − y1 = , or − = m= x2 − x1 5−0 5 5 41. We have the points (2009, 945) and (1998, 425). We ﬁnd the average rate of change, or slope.

39. From the graph we see that, when the input is −4, the output is 3, so s(−4) = 3. When the input is −2, the 63. We can substitute any real number in the numerator, but we must avoid inputs that make the denominator 0. We ﬁnd these inputs. Copyright © 2013 Pearson Education, Inc. 2 35 x2 − 7x = 0 79. x(x − 7) = 0 x = 0 or x − 7 = 0 x = 0 or x=7 The domain is {x|x = 0 and x = 7}, or (−∞, 0) ∪ (0, 7) ∪ (7, ∞). 65. We can substitute any real number for x. Thus, the domain is the set of all real numbers, or (−∞, ∞).

### An introduction to the theory of field extensions by Samuel Moy

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