   SEARCH HOME Math Central Quandaries & 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,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.