Proportional Relationships - SSAT Middle Level Quantitative

1. Identify $k$ in the proportional equation $y = \frac{3}{5}x$.

   $k = \frac{3}{5}$. The constant k is the coefficient multiplying x in the given equation.

2. Find $x$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $y = 28$.

   $x = 36$. Divide y by the ratio or multiply by its reciprocal to find x.

3. What is the equation of a proportional relationship through $(0,0)$ and $(4,10)$?

   $y = \frac{5}{2}x$. The line through origin and the point has slope k equal to y/x.

4. What is $x$ if $y$ is proportional to $x$ with $k = 4$ and $y = 52$?

   $x = 13$. Rearrange the proportional equation to solve for x by dividing y by k.

5. What is the cross-multiplication setup for solving $\frac{a}{b} = \frac{c}{d}$?

   $ad = bc$. Cross-multiplication equates the product of one fraction's numerator and the other's denominator.

6. What is the constant of proportionality $k$ in the equation $y = kx$?

   $k = \frac{y}{x}$ (for any pair with $x \ne 0$). The constant k represents the fixed ratio of y to x in any corresponding pair of values.

7. What is the missing value $y$ in the proportion $\frac{9}{12} = \frac{y}{20}$?

   $y = 15$. Cross-multiply or simplify the left ratio and scale to solve for y.

8. What is $y$ if $y$ is proportional to $x$ with $k = 7$ and $x = 3$?

   $y = 21$. Substitute the given k and x into the proportional equation y = kx.

9. Identify the missing value $x$: $\frac{12}{x} = \frac{3}{8}$.

   $x = 32$. Cross-multiplying the proportion isolates and solves for x.

10. Which value of $k$ makes $y$ proportional to $x$ if $(x,y) = (9,6)$?

    $k = \frac{6}{9} = \frac{2}{3}$. k is the reduced fraction of y divided by x from the provided pair.

11. Find $x$ if $y = \frac{3}{5}x$ and $y = 18$.

    $x = 30$. Divide y by the constant ratio or multiply by its reciprocal to solve for x.

12. Identify the missing value $y$: $\frac{y}{8} = \frac{3}{4}$.

    $y = 6$. Cross-multiplying or scaling the right side by 8 yields the value of y.

13. Find $y$ if the proportional equation is $y = \frac{5}{2}x$ and $x = 6$.

    $y = 15$. Substitute the given x into the equation to compute y.

14. Is the table proportional if $(x,y)$ includes $(3,8)$ and $(6,15)$? Answer yes or no.

    No, because $\frac{8}{3} \ne \frac{15}{6}$. Unequal ratios of y to x show the relationship is not proportional.

15. Identify the missing value $x$: $\frac{5}{x} = \frac{15}{12}$.

    $x = 4$. Cross-multiplying the proportion solves for the unknown denominator x.

16. What equation solves a proportional relationship if you know $k$ and $x$?

    $y = kx$. This equation expresses y as the product of the constant of proportionality and x.

17. Find $y$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $x = 27$.

    $y = 21$. Multiply the given x by the constant ratio to determine y.

18. Is the table proportional if $(x,y)$ includes $(2,6)$ and $(5,15)$? Answer yes or no.

    Yes, because $\frac{6}{2} = \frac{15}{5} = 3$. Equal ratios of y to x for both pairs indicate a constant of proportionality.

19. Find $y$ if $y = \frac{3}{5}x$ and $x = 20$.

    $y = 12$. Multiply the given x by the constant ratio to find y.

20. What is $k$ if a table includes the pair $(x,y) = (6,15)$ and is proportional?

    $k = \frac{15}{6} = \frac{5}{2}$. The constant k is determined by dividing y by x from the given proportional pair.

21. Identify the missing value $y$: $\frac{y}{14} = \frac{5}{7}$.

    $y = 10$. Solve the proportion by cross-multiplying or scaling the numerator.

22. What equation solves a proportional relationship if you know $k$ and $y$?

    $x = \frac{y}{k}$. Rearranging the proportional equation isolates x by dividing y by the constant k.

23. What does it mean for two quantities $x$ and $y$ to be proportional?

    $\frac{y}{x}$ is constant (equivalently, $y = kx$ for some constant $k$). Proportional quantities maintain a constant ratio, allowing representation as y equaling a constant multiple of x.

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