Question

To shop a package, a company charges a one-time fee plus a fee based on the weight of the

table shows the total shipping costs for four packages of different weights.
Shipping Costs
Weight of Package Total Shipping Cost
(pounds)
(dollars)
4
$11.00
8
$17.00
12
$23.00
16
$29.00
What equation represents the total shipping cost, C, in dollars, of a package weighing w pounds?
Complete the missing values in the equation below.
w+

Answer 1

C = 1.5w + 5

Explanation:

Look at any 2 weights and costs.

For example, look at 4 lb for $11 and 8 lb for $17.

These two pieces of information can be used as two points on a line.

The points are: (4, 11) and (8, 17)

Now we need to find the equation of the line that passes through points (4, 11) and (8, 17).

We use the slope-intercept form of the equation of a line.

y = mx + b

We find the slope:

m = (y_2 - y_1)/(x_2 - x_1) = (17 - 11)/(8 - 4) = 1.5

y = 1.5x + b

Use one point, (4, 11) for x and y, and solve for b.

11 = 1.5 × 4 + b

b = 5

The equation is

y = 1.5x + 5

Since we are using C for cost and w for pounds, we write the expression as:

C = 1.5w + 5