Question

the graph represents the balance in imena’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:

Step1: Analyze Question 7

A proportional relationship has a graph that passes through the origin \((0,0)\). The given graph has a y - intercept (when \(x = 0\)) of \(450\) (since at day \(0\), the balance is \(450\) dollars), so it does not pass through the origin. Thus, the relationship is non - proportional. So the statement in question 7 is True.

Step2: Analyze Question 8

A linear relationship has a constant rate of change (constant slope) and its graph is a straight line. The given graph is a straight line, and as the number of days (\(x\)) increases, the balance (\(y\)) decreases. The slope of a line is calculated as \(\frac{\Delta y}{\Delta x}\). Since \(\Delta y\) is negative (balance decreases) and \(\Delta x\) is positive (days increase), the slope is negative. So the graph represents a linear relationship with a negative slope, and the statement in question 8 is True.

Step3: Analyze Question 9

The general form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. From the graph, the y - intercept \(b = 450\). Let's calculate the slope. We can take two points, say \((0,450)\) and \((8,250)\). The slope \(m=\frac{250 - 450}{8-0}=\frac{- 200}{8}=- 25\). So the equation of the line should be \(y=-25x + 450\), not \(y = 450x-25\). So the statement in question 9 is False.

Answer:

1. True
2. True
3. False