Question

graph a
graph b
which statements are true about the graphs? select all that apply.
the relationship in graph b is a proportional relationship.
both graphs show proportional relationships.
an equation that represents graph a is $y = \frac{10}{7}x$.
the relationship in graph b has a constant rate of change.
both graphs show linear relationships.

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship has the form \( y = kx \) (passes through the origin). Graph A passes through \((0,0)\), so it's proportional. Graph B has a y - intercept of 2 (passes through \((0,2)\)), so it's not proportional. So "The relationship in Graph B is a proportional relationship" and "Both graphs show proportional relationships" are false.

Step2: Recall Linear and Constant Rate

A linear relationship has a constant rate of change (slope). Both Graph A and Graph B are straight lines, so they are linear. A straight line has a constant rate of change. So "The relationship in Graph B has a constant rate of change" and "Both graphs show linear relationships" are true.

Step3: Check Graph A's Equation

For Graph A, when \( x = 7 \), from the graph, \( y = 10 \) (approx). The slope \( k=\frac{y}{x}=\frac{10}{7}\), so the equation \( y=\frac{10}{7}x \) is correct.

Answer:

• The relationship in Graph B has a constant rate of change.
• Both graphs show linear relationships.
• An equation that represents Graph A is \( y = \frac{10}{7}x \)