Question

two students created the graphs shown below.
raul
becky

1. both graphs represent linear relationships.
2. both graphs have a positive slope.
3. both graphs represent proportional relationships between x and y.

Explanation:

Step1: Analyze Statement 1

A linear relationship is represented by a straight line. Both Raul's and Becky's graphs are straight lines, so this statement is true.

Step2: Analyze Statement 2

A positive slope means the line rises from left to right. Raul's line falls from left to right (negative slope), while Becky's rises (positive slope). So not both have positive slopes, this statement is false.

Step3: Analyze Statement 3

A proportional relationship (direct variation) has a graph passing through the origin \((0,0)\). Raul's graph does not pass through the origin (it intersects the y - axis above or below the origin), while Becky's does. So not both represent proportional relationships, this statement is false.

Answer:

1. True
2. False
3. False