Question

the table gives some sample data for two quantities, x and y, that are in a proportional relationship. type the answers in the boxes below. a. complete the table. x | y 14 | 21 64 | blank blank | 39 1 | blank

Explanation:

Step1: Find the constant of proportionality

For proportional relationship \( y = kx \), from \( x = 14 \), \( y = 21 \), we get \( k=\frac{y}{x}=\frac{21}{14}=\frac{3}{2} \).

Step2: Calculate \( y \) when \( x = 64 \)

Using \( y = kx \) with \( k=\frac{3}{2} \) and \( x = 64 \), \( y=\frac{3}{2}\times64 = 96 \).

Step3: Calculate \( x \) when \( y = 39 \)

From \( y = kx \), \( x=\frac{y}{k}=\frac{39}{\frac{3}{2}}=39\times\frac{2}{3}=26 \).

Step4: Calculate \( y \) when \( x = 1 \)

Using \( y = kx \) with \( k=\frac{3}{2} \) and \( x = 1 \), \( y=\frac{3}{2}\times1=\frac{3}{2}=1.5 \).

Answer:

For \( x = 64 \), \( y = 96 \); for \( y = 39 \), \( x = 26 \); for \( x = 1 \), \( y = 1.5 \) (or \( \frac{3}{2} \)). So the completed table values (from top to bottom for the empty \( y \) and \( x \) and \( y \)) are 96, 26, 1.5.