Question

total cost
9
8
7
(2, 7)
6
5
4
3
2
1
1 2 3 4 5 x
number of issues

\\(y = x + \frac{2}{7}\\)

\\(y = x + \frac{7}{2}\\)

\\(y = \frac{2}{7}x\\)

\\(y = \frac{7}{2}x\\)

Explanation:

Identify the key features of the graph

Using the Graphing Proportional Relationships knowledge point
The graph displays a straight line passing through the origin \((0,0)\), which represents a proportional relationship between the number of issues \(x\) and the total cost \(y\). We are given a specific point on this line: \((2, 7)\).

Calculate the constant of proportionality

Using the Constant of Proportionality knowledge point

$$ k = \frac{y}{x} = \frac{7}{2} $$

Write the proportional equation

Using the Proportional Relationship Equation knowledge points

$$ y = kx \implies y = \frac{7}{2}x $$

Answer:

• (A) \(y = x + \frac{2}{7}\)
• (B) \(y = x + \frac{7}{2}\)
• (C) \(y = \frac{2}{7}x\)
• (D) \(y = \frac{7}{2}x\) (Correct answer)