Question

for exercises 2 and 3, circle the correct answer. choose all that apply. 2. which of the following ratios are proportional to $\frac{16}{5}$? a. $\frac{8}{5}$ b. $\frac{32}{10}$ c. $\frac{48}{10}$ d. $\frac{80}{25}$ 3. which of the following graphs show proportional relationships? a. graph with cost ($) on y - axis and pounds on x - axis with a non - linear line b. graph with cost ($) on y - axis and pounds on x - axis with a decreasing linear line c. graph with cost ($) on y - axis and pounds on x - axis with a non - linear line d. graph with cost ($) on y - axis and pounds on x - axis with an increasing linear line through the origin lesson 2 identify proportional relationships

Explanation:

Step1: Simplify ratios for question 2

For a ratio $\frac{a}{b}$ to be proportional to $\frac{16}{5}$, the cross - products should be equal or the simplified form should be the same.

• For option a: $\frac{8}{5}

eq\frac{16}{5}$.

• For option b: Simplify $\frac{32}{10}=\frac{16\times2}{5\times2}=\frac{16}{5}$.
• For option c: Simplify $\frac{48}{10}=\frac{24}{5}

eq\frac{16}{5}$.

• For option d: Simplify $\frac{80}{25}=\frac{16\times5}{5\times5}=\frac{16}{5}$.

Step2: Recall properties of proportional graphs for question 3

A proportional relationship has a graph that is a straight - line passing through the origin $(0,0)$.

• Option a: The line does not pass through the origin, so it is not a proportional relationship.
• Option b: The line is decreasing and does not represent a proportional relationship (proportional relationships have a constant positive or negative ratio, and the graph should be a non - vertical straight line through the origin).
• Option c: The line does not pass through the origin, so it is not a proportional relationship.
• Option d: The line is a straight line passing through the origin, so it represents a proportional relationship.

Answer:

1. b. $\frac{32}{10}$, d. $\frac{80}{25}$
2. d.