1. Write the point-slope form for the line with slope $\frac{6}{5}$ through point $(-4,-2)$. Using the formula $y - y_1 = m(x - x_1)$, substitute $m = \frac{6}{5}$, $x_1 = -4$, $y_1 = -2$: $$y - (-2) = \frac{6}{5}(x - (-4)) \implies y + 2 = \frac{6}{5}(x + 4)$$ 2. For the given problems, substitute slope and points into point-slope form: 1) $m = -\frac{2}{3}$, point $(8,12)$: $$y - 12 = -\frac{2}{3}(x - 8)$$ 2) $m = -\frac{5}{2}$, point $(2,15)$: $$y - 15 = -\frac{5}{2}(x - 2)$$ 3) $m = -8$, point $\left(\frac{2}{3}, -\frac{4}{5}\right)$: $$y + \frac{4}{5} = -8\left(x - \frac{2}{3}\right)$$ 4) $m = -13$, point $\left(-\frac{7}{2}, \frac{6}{11}\right)$: $$y - \frac{6}{11} = -13\left(x + \frac{7}{2}\right)$$ 5) $m = 1.4$, point $(-2.5, 3.5)$: $$y - 3.5 = 1.4(x + 2.5)$$ 6) $m = 0.7$, point $(4.5, -6.5)$: $$y + 6.5 = 0.7(x - 4.5)$$ 7) $m = 0.5$, point $(-1.25, 2.75)$: $$y - 2.75 = 0.5(x + 1.25)$$ 8) $m = -0.75$, point $(-1.5, -3)$: $$y + 3 = -0.75(x + 1.5)$$ 9) $m = 0.125$, point $(-4, -8)$: $$y + 8 = 0.125(x + 4)$$ 3. Write the lines directly given: 10) $y - 2 = x - 1$ 11) $y + 3 = 2(x - 1)$ 12) $y + 3 = \frac{2}{3}(x - 3)$ 4. Find slope and write point-slope form for pairs of points: 13. $m = \frac{6-8}{-4-2} = \frac{-2}{-6} = \frac{1}{3}$, point $(2,8)$: $$y - 8 = \frac{1}{3}(x - 2)$$ 14. $m = \frac{3 - 11}{-6 - 5} = \frac{-8}{-11} = \frac{8}{11}$, point $(5,11)$: $$y - 11 = \frac{8}{11}(x - 5)$$ 15. $m = \frac{14 - 7}{4 - (-3)} = \frac{7}{7} = 1$, point $(-3,7)$: $$y - 7 = 1(x + 3)$$ 16. $m = \frac{-4 - (-6)}{5 - 4} = \frac{2}{1} = 2$, point $(4,-6)$: $$y + 6 = 2(x - 4)$$ 17. $m = \frac{-5 - 2}{8 - 6} = \frac{-7}{2}$, point $(6,2)$: $$y - 2 = -\frac{7}{2}(x - 6)$$ 18. $m = \frac{-10 - (-9)}{13 - (-12)} = \frac{-1}{25}$, point $(-12,-9)$: $$y + 9 = -\frac{1}{25}(x + 12)$$ 19. $m = \frac{-5.1 - 1.9}{-3.8 - 5.2} = \frac{-7}{-9} = \frac{7}{9}$, point $(5.2,1.9)$: $$y - 1.9 = \frac{7}{9}(x - 5.2)$$ 20. Convert mixed numbers: $(3\tfrac{1}{2}, 2\tfrac{2}{3}) = (3.5, 2.666...)$, $(6\tfrac{1}{2}, -1\tfrac{1}{3}) = (6.5, -1.333...)$ Slope: $m = \frac{-1.333... - 2.666...}{6.5 - 3.5} = \frac{-4}{3} = -\frac{4}{3}$ Point $(3.5, 2.666...)$: $$y - 2.666... = -\frac{4}{3}(x - 3.5)$$ 21. Convert and find slope: $(4\tfrac{1}{5}, 6\tfrac{3}{4}) = (4.2, 6.75)$, $(-2\tfrac{4}{5}, 8\tfrac{3}{4}) = (-2.8, 8.75)$ Slope: $m = \frac{8.75 - 6.75}{-2.8 - 4.2} = \frac{2}{-7} = -\frac{2}{7}$ Point $(4.2, 6.75)$: $$y - 6.75 = -\frac{2}{7}(x - 4.2)$$ 22.a. Using visits and cost, set linear model: Cost = Monthly Fee + Co-pay $\times$ Visits Using April and May data: $135.75 = F + 4c$, $94.75 = F + 2c$ Subtract: $135.75 - 94.75 = 4c - 2c \Rightarrow 41 = 2c \Rightarrow c = 20.5$ Co-pay = 20.5 per visit. 22.b. For 7 visits: Cost = $F + 7 \times 20.5$ From May: $94.75 = F + 2 \times 20.5 = F + 41 \Rightarrow F = 53.75$ Cost = $53.75 + 7 \times 20.5 = 53.75 + 143.5 = 197.25$ 23. Multiply $-95 \times 32 = -3040$ 24. Multiply $2 \times 7\frac{1}{8} = 2 \times \frac{57}{8} = \frac{114}{8} = 14.25$ 25. Multiply $19.9 \times 4.5 = 89.55$ Final answers are the point-slope equations and computations above. Graphs are described but must be drawn separately on paper.