Answer: (43) 16
(44) y = -(9/4)x = 6
(45) parallel: y = 2x - 4
perpendicular: y = -(1/2)x - 5/2
Step-by-step explanation:
43) f(x) = (1/3)x + 8
f(-12) = (1/3)(-12) + 8
= -4 + 8
= 4
3f(-12) = 3(4)
= 12
3f(-12) + 4 = 12 + 4
= 16
44) slope (m) = [tex]\dfrac{-3-(-12)}{4-8}=\dfrac{9}{-4}[/tex]
[tex]y-y_1=m(x-x_1)\\\\\\y-(-3)=-\dfrac{9}{4}(x-4)\\\\\\y+3=-\dfrac{9}{4}x+9\\\\\\y=-\dfrac{9}{4}x+6[/tex]
45) parallel is same slope → m = 2
perpendicular is opposite reciprocal slope → [tex]m=-\dfrac{1}{2}[/tex]
parallel
[tex]y-y_1=m(x-x_1)\\\\\\y-(-2)=2(x-1)\\\\\\y+2=2x-2\\\\\\y=2x-4[/tex]
perpendicular
[tex]y-y_1=m(x-x_1)\\\\\\y-(-2)=-\dfrac{1}{2}(x-1)\\\\\\y+3=-\dfrac{1}{2}x+\dfrac{1}{2}\\\\\\y=-\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
