Final answer:
To write the linear equation for the situation where y is the total cost for x batteries, use the cost per battery derived from the given information ($0.90), resulting in the equation y = 0.90x.
Step-by-step explanation:
To find the linear equation for the cost of x batteries, we first need to determine the cost per battery. We can use the given information: five batteries cost $4.50 and seven batteries cost $6.30. By dividing the total cost by the number of batteries, we find the cost per battery is $0.90 from the first scenario (since $4.50 ÷ 5 = $0.90) and approximately $0.90 from the second scenario as well (since $6.30 ÷ 7 ≈ $0.90). This confirms a consistent price per battery.
Now, we will use this cost per battery to write the linear equation. If y is the total cost for x batteries:
y = 0.90x
This equation indicates that for every additional battery purchased, the total cost increases by $0.90. Here, the slope is $0.90, which represents the rate of change in cost with respect to the number of batteries. The y-intercept is zero, since if no batteries are bought, the cost is $0.