Question

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

c the graph represents the balance in jimena’s checking account based on the number of days since her last paycheck.

1. the relationship shown on the graph is non - proportional.
2. the graph represents a linear relationship with a negative slope.
3. the graph can be represented by y = 450x - 25.

Explanation:

Question 7

Step1: Recall proportional relationship

A proportional relationship has the form \( y = kx \) (passes through the origin \((0,0)\)).

Step2: Analyze the graph

The graph starts at \((0, 450)\), not \((0,0)\). So it’s non - proportional.

Step1: Recall linear relationship

A linear relationship is a straight line (constant slope).

Step2: Check the graph

The graph is a straight line, so it’s linear. The slope is negative (decreasing from left to right).

Step1: Find the slope

Two points: \((0, 450)\) and \((8, 200)\). Slope \( m=\frac{200 - 450}{8 - 0}=\frac{- 250}{8}=-31.25\).

Step2: Check the equation

The equation \( y = 450x-25\) has slope \( 450\) (positive), but the graph has a negative slope. So it’s false.

Answer:

True (The relationship is non - proportional)

Question 8