Answer:
[tex]\displaystyle \perp\:y = -\frac{4}{7}x + 6\frac{4}{7} \\ \parallel\:y = 1\frac{3}{4}x - 12[/tex]
Step-by-step explanation:
Perpendicular equations have OPPOCITE MULTIPLICATIVE INVERCE RATE OF CHANGES [SLOPES], so 1¾ becomes −⁴⁄₇, and we move forward:
[tex]\displaystyle 2 = -\frac{4}{7}[8] + b \hookrightarrow 2 = -4\frac{4}{7} + b; 6\frac{4}{7} = b \\ \\ \boxed{y = -\frac{4}{7}x + 6\frac{4}{7}}[/tex]
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so 1¾ remains as is as we proceed:
[tex]\displaystyle 2 = 1\frac{3}{4}[8] + b \hookrightarrow 2 = 14 + b; -12 = b \\ \\ \boxed{y = 1\frac{3}{4}x - 12}[/tex]
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