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chapter 1 11

# chapter 1 11 - SECTION 1.2 MATHEMATICAL MODELS D 11 b = 3 b...

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Unformatted text preview: SECTION 1.2 MATHEMATICAL MODELS D 11 b = 3 b = O 5. (a) An equation for the family of linear functions with slope 2 is y = f(m) = 2m + b, where b is the y—intercept. (b) f(2) = 1 means that the point (2, 1) is on the graph of f. We can use the point-slope form of a line to obtain an equation for the family of linear functions through the point (27 1). y — 1 : m (:7: — 2), which is equivalent to y : man + (1 — 2m) in slope—intercept form. (c) To belong to both families, an equation must have slope m = 2, so the equation in part (b), y 2 mac + (1 — 2m), becomes y : 2m ~ 3. It is the only function that belongs to both families. 6. All members of the family of linear functions f (w) = 1 + m(:r + 3) have graphs that are lines passing through the point (—3, 1). 7. All members of the family of linear functions f (cc) 2 c — a: have graphs that are lines with slope —1. The y—intercept is c. 8. (a) (b) The slope of —4 means that for each increase of 1 dollar for a rental space. the number of spaces rented decreases by 4. The y—intercept of 200 is the number of spaces that would be occupied if there were no charge for each space. The x-intercept of 50 is the smallest rental fee that results in no spaces rented. 0102030405060" ...
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