the table shows the total cost of purchasing x same - priced items and a catalog. what is the initial value…

Explanation:

Step1: Find the cost per item

The cost per item is the slope of the linear - relationship. When the number of items $x$ changes from 1 to 2 ( $\Delta x=2 - 1 = 1$), the total cost $y$ changes from 10 to 14 ( $\Delta y=14 - 10 = 4$). The cost per item $m=\frac{\Delta y}{\Delta x}=4$.

Step2: Find the initial value

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept (initial value). Using the point $(x = 1,y = 10)$ and $m = 4$, we substitute into the equation $y=mx + b$: $10=4\times1 + b$. Solving for $b$ gives $b = 10-4=6$. The initial value is the cost when $x = 0$, which represents the cost of the catalog.

Answer:

$6, the cost of the catalog