Question

lesson 2: homework
notes or additional instructions based on whole-class discussion of homework assignment.

1. what are important graphical features of proportional relationships? circle all correct statements

a. the graph is a straight line.
b. the line has a y-intercept of 0.
c. the line passes through the origin.
d. the line has an x-intercept of 0.
e. the line passes through the point (0,0).
use the graph to answer questions 2–5.

1. which lines represent proportional relationships?

explain how you know.

1. find the rate of change for each line.

a:
b:
c:
d:
e:

Explanation:

Step1: Recall Proportional Relationship Graphs

Proportional relationships are linear (straight lines) and pass through the origin \((0,0)\) (so \(y\)-intercept, \(x\)-intercept, and the point \((0,0)\) are all \(0\) or the origin). So lines representing proportional relationships must be straight and pass through \((0,0)\).

Step2: Analyze Each Line

• Line A: Straight and passes through \((0,0)\) (origin).
• Line B: Straight but has a \(y\)-intercept of \(4\) (does not pass through origin), so not proportional.
• Line C: Straight and passes through \((0,0)\).
• Line D: Straight and passes through \((0,0)\).
• Line E: Straight and passes through \((0,0)\).

Answer:

Lines A, C, D, and E represent proportional relationships. This is because proportional relationships are linear (straight lines) and pass through the origin \((0,0)\). Line B is straight but has a \(y\)-intercept of \(4\) (does not pass through the origin), so it is not a proportional relationship.