Math CentralQuandaries & Queries


Question from Coco:

Good afternoon
If relationship between total cost and the number of units made it linear ,and if costs increases by $7\$$ for each additional unit made ,and if the total cost of 10 units is $180\$$ .
Find the equation of the relationship b/n total cost (Y) & number of unit made (x).

The cost for 10 units is $180\$$ and since the cost increases $7\$$ for each additional unit made the cost for 11 units will be $187\$,$ and the cost for 12 units will be $194\$,$ and so on. This $7\$$ increase for each additional unit made is exactly the slope of the relationship, 7 dollars per unit. This slope is commonly called $m$ so $m = 7\$$ per unit.

To complete the equation of the line you need to know the Y-intercept, that is the cost when the number of units produced is $0.$ Starting at 10 units produced the total cost decreases $10\$$ for each fewer items you make. A decrease to $0$ items is a decrease of $10$ units so the total cost decreases $10 \times 7\$ = 70\$.$ Hence the Y-intercept is $180\$ - 70\$ = 110\$.$

I hope this helps,

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