The 1980s saw a trend toward old-fashioned punitive deterrence in contrast to the more liberal penal policies and community-based corrections that were popular in the 1960s and early 1970s. as a result, prisons became more crowded, and the gap between the number of people in prison and prison capacity widened. based on figures from a certain government agency, the number of prisoners (in thousands) in federal and state prisons is approximately 3.9t2 + 26.8t + 436.3 (0 ≤ t ≤ 10) and the number of inmates (in thousands) for which prisons were designed is given by 24.2t + 363 (0 ≤ t ≤ 10) where t is measured in years, and t = 0 corresponds to 1984. find an expression giving the gap between the number of prisoners and the number for which the prisons were designed at any time t.

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|