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For each table, determine whether it shows a direct variation, an inverse variation, or neither.
Write the equation for the direct or inverse variation when it exists.
(a)
(b)

x

y

4
1

5
1.25

7
1.75

Direct variation
Equation:
◻

x

y

2
21

3
14

6
7

Direct variation
Equation:
◻
Inverse variation
Inverse variation
Equation:
◻ Equation:
◻
Neither
Check
2024 McGraw Hill LLC. All Rights R
Desk 1

For each table, determine whether it shows a direct variation, an inverse variation, or neither. $\newline$ Write the equation for the direct or inverse variation when it exists. $\newline$ (a) $\newline$ (b) $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline $x$ & $y$ \\ $\newline$ \hline $4$ & $1$ \\ $\newline$ \hline $5$ & $1$ . $25$ \\ $\newline$ \hline $7$ & $1$ . $75$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Direct variation $\newline$ Equation: $\square$ $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline $x$ & $y$ \\ $\newline$ \hline $2$ & $21$ \\ $\newline$ \hline $3$ & $14$ \\ $\newline$ \hline $6$ & $7$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Direct variation $\newline$ Equation: $\square$ $\newline$ Inverse variation $\newline$ Inverse variation $\newline$ Equation: $\square$ Equation: $\square$ $\newline$ Neither $\newline$ Check $\newline$ $2024$ McGraw Hill LLC. All Rights R $\newline$ Desk $1$

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Math Problems

Grade 8

Evaluate a linear function: word problems

Full solution

Q. For each table, determine whether it shows a direct variation, an inverse variation, or neither.

\newline

Write the equation for the direct or inverse variation when it exists.

\newline

(a)

\newline

(b)

\newline

\begin{tabular}{|c|c|}

\newline

\hline

x

y

\newline

\hline

4

1

\newline

\hline

5

1

25

\newline

\hline

7

1

75

\newline

\hline

\newline

\end{tabular}

\newline

Direct variation

\newline

Equation:

\square

\newline

\begin{tabular}{|c|c|}

\newline

\hline

x

y

\newline

\hline

2

21

\newline

\hline

3

14

\newline

\hline

6

7

\newline

\hline

\newline

\end{tabular}

\newline

Direct variation

\newline

Equation:

\square

\newline

Inverse variation

\newline

Inverse variation

\newline

Equation:

\square

Equation:

\square

\newline

Neither

\newline

Check

\newline

2024

McGraw Hill LLC. All Rights R

\newline

Desk

1

Check Direct Variation: For table (a), check if $y$ varies directly with $x$ by dividing $y$ by $x$ for each pair to see if the ratio is constant.
Calculate Ratio - Pair $1$ : Calculate the ratio for the first pair: $y/x = 1/4 = 0.25$ .
Calculate Ratio - Pair $2$ : Calculate the ratio for the second pair: $y/x = 1.25/5 = 0.25$ .
Calculate Ratio - Pair $3$ : Calculate the ratio for the third pair: $y/x = 1.75/7 = 0.25$ .
Direct Variation Equation: Since the ratio $y/x$ is constant ( $0.25$ ) for all pairs, table (a) shows a direct variation.
Check Inverse Variation: The equation for the direct variation is $y = kx$ , where $k$ is the constant ratio. Here, $k = 0.25$ , so the equation is $y = 0.25x$ .
Calculate Product - Pair $1$ : For table (b), check if $y$ varies inversely with $x$ by multiplying $y$ by $x$ for each pair to see if the product is constant.
Calculate Product - Pair $2$ : Calculate the product for the first pair: $xy = 2 \times 21 = 42$ .
Calculate Product - Pair $3$ : Calculate the product for the second pair: $xy = 3 \times 14 = 42$ .
Inverse Variation Equation: Calculate the product for the third pair: $xy = 6 \times 7 = 42$ .
Inverse Variation Equation: Calculate the product for the third pair: $xy = 6 \times 7 = 42$ .Since the product $xy$ is constant ( $42$ ) for all pairs, table (b) shows an inverse variation.
Inverse Variation Equation: Calculate the product for the third pair: $xy = 6 \times 7 = 42$ .Since the product $xy$ is constant ( $42$ ) for all pairs, table (b) shows an inverse variation.The equation for the inverse variation is $xy = k$ , where $k$ is the constant product. Here, $k = 42$ , so the equation is $xy = 42$ .