Question

While surfing the Internet, you find a site that claims to offer the most popular and the cheapest DVDs anywhere. Unfortunately, the website isn't clear about how much they charge for each DVD, but it does give you the following information:

Number of DVDs Ordered
1 is $15, Two DVDs - $24, and Three DVDs - $33 (includes S&H)

a. *Plot the points and connect them to form a line.*
b. *What is the slope of the line containing the data points?*
c. *What does the slope represent in this problem?*
d. *What is the y-intercept of the line that contains the data points?*

a) Upward sloping line
b) 3
c) Cost per DVD
d) $9

Answer 1

a) To plot the points and connect them to form a line, we can use a graph. Let's plot the points (1, 15), (2, 24), and (3, 33) on a coordinate plane. The x-axis represents the number of DVDs ordered, and the y-axis represents the cost.

b) To find the slope of the line containing the data points, we can use the formula: slope = (change in y)/(change in x). Let's choose two points on the line, (1, 15) and (3, 33). The change in y is 33 - 15 = 18, and the change in x is 3 - 1 = 2. Therefore, the slope is 18/2 = 9.

c) In this problem, the slope represents the cost per DVD. For every increase in the number of DVDs ordered, the cost increases by the slope value, which is $9. So, the slope represents the rate at which the cost per DVD increases.

d) To find the y-intercept of the line that contains the data points, we can use the formula: y-intercept = y - slope*x. Let's choose a point on the line, for example, (1, 15). Substituting the values into the formula, we have: y-intercept = 15 - 9*1 = 6. Therefore, the y-intercept of the line is $6.

To summarize:

a) Plot the points (1, 15), (2, 24), and (3, 33) on a graph and connect them to form a line.

b) The slope of the line containing the data points is 9.

c) In this problem, the slope represents the cost per DVD, which increases by $9 for every increase in the number of DVDs ordered.

d) The y-intercept of the line that contains the data points is $6.

Step-by-step explanation:

Answer 2

To plot the points, connect them to create a line. The slope of the line is 9, representing the cost per DVD. The y-intercept of the line is $9.

Step-by-step explanation:

To plot the points, we can use a graph where the x-axis represents the number of DVDs ordered and the y-axis represents the cost. The three points given are (1, 15), (2, 24), and (3, 33). We can connect these points to form a line.

The slope of the line can be found using the formula: slope = Δy / Δx, where Δy is the change in y-values and Δx is the change in x-values. In this case, Δy = 33 - 15 = 18 and Δx = 3 - 1 = 2. Therefore, the slope = 18 / 2 = 9.

The slope represents the cost per DVD. In this case, the slope is 9, which means that for each additional DVD ordered, the cost increases by $9.

The y-intercept is the value of y when x = 0. In this case, when no DVDs are ordered, the cost is $9. Therefore, the y-intercept is $9.