Question

the graph shows the relationship between the total cost and the number of erasers bought at the student store. which statement is true? each eraser costs $1.00 each eraser costs $1.50 three erasers cost $6. seven erasers cost $3.50.

Explanation:

Step1: Find the cost per eraser

Let's take two points from the graph. For example, when \(x = 2\) (number of erasers), \(y=1\) (total cost in dollars). The unit - rate (cost per eraser) is calculated as \(r=\frac{y}{x}\). Using the point \((2,1)\), \(r = \frac{1}{2}=0.5\) is incorrect. Let's check another way.
If we assume the relationship is linear \(y = mx\) (since it passes through the origin \((0,0)\)).
Take the point \((3,1.5)\), then \(m=\frac{y}{x}=\frac{1.5}{3}=0.5\) (wrong for the first two options).
Take the point \((7,3.5)\)

Step2: Calculate the cost for 7 erasers

Using the formula \(y = mx\), where \(m\) is the cost per eraser. If \(x = 7\) and \(y=3.5\), and \(m=\frac{y}{x}=\frac{3.5}{7}=0.5\). The cost of 7 erasers: \(y=0.5\times7 = 3.5\)

Answer:

Seven erasers cost \(\$3.50\)