Proportional relationships (constant of proportionality, graphs, equations) Knowledge-Based Download PDF

Questions

1. 1.

   In a proportional relationship, the constant of proportionality relating $y$ to $x$ is $\frac{3}{8}$. What is the constant of proportionality relating $x$ to $y$?

   • A) $\frac{3}{8}$
   • B) $\frac{5}{8}$
   • C) $\frac{8}{3}$
   • D) $-\frac{3}{8}$
2. 2.

   Which set of ordered pairs represents a proportional relationship between $x$ and $y$?

   • A) $\{(2, 6), (4, 10), (6, 14)\}$
   • B) $\{(3, 9), (5, 15), (8, 20)\}$
   • C) $\{(1, 4), (2, 7), (3, 10)\}$
   • D) $\{(4, 14), (6, 21), (10, 35)\}$
3. 3.

   In a proportional relationship between an independent variable $x$ and a dependent variable $y$, the constant of proportionality is $k$. Which ordered pair on the graph of this relationship always has the constant of proportionality as its $y$-coordinate?

   • A) $(0, k)$
   • B) $(k, 1)$
   • C) $(1, k)$
   • D) $(k, k)$
4. 4.

   Which of the following equations represents a proportional relationship between $x$ and $y$?

   • A) $y = \frac{3}{8}x$
   • B) $y = \frac{3}{8}x + 5$
   • C) $y = \frac{3}{8x}$
   • D) $y = \frac{3}{8}x^2$
5. 5.

   In a proportional relationship between $x$ and $y$, $y = 36$ when $x = 24$. What is the value of $y$ when $x = 10$?

   • A) $\frac{20}{3}$
   • B) 12
   • C) 15
   • D) 22
6. 6.

   A proportional relationship between $x$ and $y$ has a constant of proportionality equal to $\frac{5}{2}$. Which of the following statements correctly describes the graph of this relationship?

   • A) The graph is a straight line passing through $(0, \frac{5}{2})$ and $(2, 0)$.
   • B) The graph is a curved line passing through the origin $(0, 0)$ and the point $(2, 5)$.
   • C) The graph is a straight line passing through the origin $(0, 0)$ and the point $(\frac{5}{2}, 1)$.
   • D) The graph is a straight line through the origin $(0, 0)$ that passes through the point $(1, \frac{5}{2})$.
7. 7.

   The equation $y = \frac{4}{9}x$ represents a proportional relationship between $x$ and $y$. Which ordered pair $(x, y)$ lies on the graph of this relationship?

   • A) $(4, 9)$
   • B) $(8, 18)$
   • C) $(27, 12)$
   • D) $(12, 27)$