Identify Proportional Relationships - 7th Grade Math

1. Find $k$ for a proportional relationship passing through $(6,15)$.

   $k = \frac{15}{6} = \frac{5}{2}$

2. What is $k$ for a proportional relationship passing through $(4,10)$ and $(0,0)$?

   $k=\frac{5}{2}$. Use $k=\frac{y}{x}=\frac{10}{4}=\frac{5}{2}$.

3. What equation form represents a proportional relationship between $x$ and $y$?

   $y = kx$

4. Find the missing value to keep proportionality: if $\frac{y}{x} = \frac{3}{4}$ and $x = 12$, what is $y$?

   $y = 9$

5. Find $x$ if $y$ is proportional to $x$ with $k=5$ and $y=35$.

   $x=7$. Solve $35=5x$ to get $x=7$.

6. Which point must be on the graph of any proportional relationship?

   $(0,0)$. The origin because when $x=0$, $y=0$ in $y=kx$.

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

   $k$. The constant that relates $y$ to $x$ in direct proportion.

8. Identify whether the table is proportional: $(2,3)$, $(4,6)$, $(6,8)$.

   No; $\frac{3}{2} \ne \frac{8}{6}$

9. Find the missing value to keep proportionality: if $\frac{y}{x} = 5$ and $x = 7$, what is $y$?

   $y = 35$

10. Identify whether the table is proportional: $(1,4)$, $(2,8)$, $(3,12)$.

    Yes; $\frac{y}{x} = 4$ each time

11. Identify whether the graph of $y = 2x$ is proportional, and state $k$.

    Proportional; $k = 2$

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

    $k = \frac{y}{x}$ for $x \ne 0$

13. Identify whether $(3,8)$ and $(9,20)$ could be in the same proportional relationship.

    No, not proportional. Different ratios: $\frac{8}{3}\approx 2.67$ vs $\frac{20}{9}\approx 2.22$.

14. Identify whether $y = -\frac{1}{2}x$ represents a proportional relationship.

    Yes; it has the form $y = kx$

15. Identify whether the relationship is proportional: $y=\frac{4}{5}x-1$.

    No, not proportional. The $-1$ makes it not pass through $(0,0)$.

16. Identify whether the points $(0,0)$, $(2,6)$, and $(3,9)$ lie on a proportional graph.

    Yes; all satisfy $y = 3x$

17. Identify whether $y = 3x + 2$ represents a proportional relationship.

    No; it does not pass through $(0,0)$

18. Choose the equation that represents a proportional relationship: $y=3x$ or $y=3x+2$.

    $y=3x$. Only $y=3x$ passes through $(0,0)$; $y=3x+2$ has $y$-intercept $2$.

19. What condition on a graph shows two quantities are proportional?

    A straight line that passes through $(0,0)$

20. What must the graph of a proportional relationship look like on a coordinate plane?

    A straight line through $(0,0)$. Proportional relationships always pass through the origin.

21. Identify whether the table is proportional: $(1,3)$, $(2,6)$, $(3,9)$.

    Yes, proportional. All ratios equal $3$: $\frac{3}{1}=\frac{6}{2}=\frac{9}{3}=3$.

22. Identify whether the points $(2,5)$ and $(4,10)$ show a proportional relationship.

    Yes; $\frac{5}{2} = \frac{10}{4}$

23. Identify whether $(0,5)$ can be on a proportional graph of $y$ vs. $x$.

    No; proportional graphs must include $(0,0)$

24. Identify whether the relationship is proportional: $x: 3,6,9$ and $y: 10,20,35$.

    No; ratios $\frac{10}{3}$, $\frac{20}{6}$, $\frac{35}{9}$ are not equal

25. Identify whether the points form a proportional relationship: $(0,0)$, $(2,5)$, $(4,10)$.

    Yes, proportional. All have constant ratio $\frac{5}{2}$ and include $(0,0)$.

26. Find $k$ for a proportional relationship passing through $(8,2)$.

    $k = \frac{2}{8} = \frac{1}{4}$

27. Which ratio test decides if a table shows proportionality for pairs $(x,y)$?

    All ratios $\frac{y}{x}$ are equal (for $x \ne 0$)

28. Identify whether $(2,7)$ and $(6,21)$ could be in the same proportional relationship.

    Yes, proportional. Both have ratio $\frac{7}{2}=\frac{21}{6}=3.5$.

29. What ratio must stay equal in a proportional relationship between $x$ and $y$?

    $\frac{y}{x}$ is constant for $x\neq 0$. In proportional relationships, all ratios of $y$ to $x$ are equal.

30. Which option must be true if $(x,y)$ pairs are proportional: A) $y-x$ constant, B) $\frac{y}{x}$ constant?

    B) $\frac{y}{x}$ is constant (for $x \ne 0$)

31. Identify whether the table is proportional: $(1,2)$, $(2,5)$, $(3,6)$.

    No, not proportional. Ratios vary: $\frac{2}{1}=2$, $\frac{5}{2}=2.5$, $\frac{6}{3}=2$.

32. Identify whether the relationship is proportional: $y=\frac{4}{5}x$.

    Yes, proportional. Form $y=kx$ with $k=\frac{4}{5}$ passes through origin.

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

    $y=kx$ for a constant $k$. Proportional means one quantity is a constant multiple of the other.

34. Identify whether the points form a proportional relationship: $(1,2)$, $(2,4)$, $(3,7)$.

    No, not proportional. Ratio changes: $\frac{2}{1}=2$, $\frac{4}{2}=2$, but $\frac{7}{3}\approx 2.33$.

35. A graph is a straight line but crosses the $y$-axis at $(0,3)$. Is it proportional?

    No, not proportional. Must pass through $(0,0)$ to be proportional.

36. Find $y$ if $y$ is proportional to $x$ with $k=\frac{3}{4}$ and $x=8$.

    $y=6$. Substitute: $y=\frac{3}{4}(8)=6$.

37. Identify whether the points $(1,3)$ and $(2,6)$ are proportional to the origin.

    Yes; $\frac{3}{1} = \frac{6}{2} = 3$

38. What is $k$ for a proportional relationship passing through $(6,4)$ and $(0,0)$?

    $k=\frac{2}{3}$. Use $k=\frac{y}{x}=\frac{4}{6}=\frac{2}{3}$.

39. Identify whether the table is proportional: $x=0,2,4$ and $y=0,6,12$.

    Yes, proportional. Constant ratio $\frac{6}{2}=\frac{12}{4}=3$ and includes $(0,0)$.

40. Identify whether the points $(2,5)$ and $(4,11)$ show a proportional relationship.

    No; $\frac{5}{2} \ne \frac{11}{4}$

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