Answer/Step-by-step explanation:
In the situation explained in the question, the cost of shipping is dependent on the weight of the box to be shipped.
For a box of 4 pounds, total shopping cost (x) => $15 (y)
For a box of 8 pounds (x), total shopping cost => $23 (y)
Therefore:
a. The input is weight of box
b. The output is cost of shipping
c. Using the 2 given pair (4, 15) and (8, 23), slope is calculate using the formula below:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{23 - 15}{8 - 4} = \frac{8}{4} = 2 [/tex]
Slope = 2
d. The slope represents the amount charged per pound of weight. That is, $2 per pound.
e. Let's derive an equation to represent the situation using the slope-intercept formula given as y = mx + b
y = total cost of shipping
x = weight of box
m = average cost per pound = slope
b = y-intercept = flat fee charged for shipping before adding the cost of weight per pound
Substitute x = 4, y = 15, m = 2 into y = mx + b, and solve for b
15 = 2(4) + b
15 = 8 + b
15 - 8 = b
7 = b
b = 7
The equation would be y = 2x + 7
The y-intercept = 7
f. The y-intercept, 7, is the starting amount, that is the flat fee charged before the cost per pound of weight of a box is added to give total cost of shipping.
