Final answer:
To determine the cost to ship a 9-pound package, the linear equation's slope and y-intercept were calculated using two given points. The resulting shipping cost function is y = 0.80x + 3.75, which reveals that shipping a 9-pound package costs $10.95.
Step-by-step explanation:
To determine the cost to ship a 9-pound package using the linear function provided, we first need to establish the slope (m) and the y-intercept (b) of the equation. We are given two points: (4, 6.95) and (7, 9.35), which represent the weight and corresponding cost of shipping.
First, calculate the slope (m):
\[m = \frac{\Delta y}{\Delta x} = \frac{(9.35 - 6.95)}{(7 - 4)} = \frac{2.40}{3} = 0.80\]
The slope, or cost per additional pound, is $0.80. Now, we use one of the points to find the y-intercept (b). Using point (4, 6.95):
\[6.95 = 0.80(4) + b\]
Solving for b gives us:\[b = 6.95 - 3.20 = 3.75\]
Now we have the equation of the line:
\[y = 0.80x + 3.75\]
Finally, substitute the weight of the 9-pound package as x to find the cost (y):
\[y = 0.80(9) + 3.75 = 7.20 + 3.75 = 10.95\]
Therefore, the cost of shipping a 9-pound package is $10.95.