Question

for each table, determine whether it shows a direct variation. if it does, write its direct variation equation. x y 4 5 8 10 16 20 ∘ not direct variation ∘ direct variation equation: x y -6 4.8 -5 4 15 -12 ∘ not direct variation ∘ direct variation equation:

Explanation:

Step1: Analyze first table

Check if \( \frac{y}{x} \) is constant. For \( x = 4, y = 5 \), \( \frac{5}{4}=1.25 \). For \( x = 8, y = 10 \), \( \frac{10}{8}=1.25 \). For \( x = 16, y = 20 \), \( \frac{20}{16}=1.25 \). Constant ratio, so direct variation. Equation: \( y = 1.25x \) or \( y=\frac{5}{4}x \).

Step2: Analyze second table

Check \( \frac{y}{x} \). For \( x=-6, y = 4.8 \), \( \frac{4.8}{-6}=-0.8 \). For \( x=-5, y = 4 \), \( \frac{4}{-5}=-0.8 \). For \( x = 15, y=-12 \), \( \frac{-12}{15}=-0.8 \). Constant ratio, so direct variation. Equation: \( y=-0.8x \) or \( y=-\frac{4}{5}x \).

Answer:

First table: Direct variation, Equation: \( y = \frac{5}{4}x \) (or \( y = 1.25x \))
Second table: Direct variation, Equation: \( y = -0.8x \) (or \( y = -\frac{4}{5}x \))