Question

Emelyn is comparing the rates of two different gardening companies for her camp site. The table below shows the rates for Log Edge Landscaping. Log Edge Landscaping Hours Worked 1.5 3 3.5 4.5 Total Cost $26 $44 $50 $62 The equation below represents the rates for Gatewood Gardening Services, where x represents the hours worked and y represents the total cost, in dollars. Compare the rates of both companies, and graph the relationship that represents the cost for the company with a greater rate of change.

Answer 1

See Explanation

Explanation:

Given

Edge Landscaping:

`\begin{array}{cc}{Hours} & {Total} & {1.5} & {\$26} & {3} & {\$44} & {3.5} & {\$50} & {4.5} & {\$62} \ \end{array}`

The rates (m) of the above table is calculated using:

`m = (y_2 - y_1)/(x_2 - x_1)`

From the table, we have the following points

`(x_1,y_1) = (1.5,26)`

`(x_1,y_1) = (4.5,62)`

So, the rate is:

`m = (62 - 26)/(4.5 - 1.5)`

`m = (36)/(3.0)`

`m = 12.0`

This means that the rate of edge landscaping is $12.0 per hour

The equation for Gatewood is not given. Hence, the rate cannot be calculated. However, the general procedure of calculating rates from a linear equation is as follows;

A linear equation is of the form:

`y = mx + b`

Where:

`m \to slope\ or\ rates`

In other words, if the equation is:

`y = 20x + 5`

Then the rate is: 20 ($20/hour)

If the equation is:
`y = 10x + 5`

Then the rate is 10 ($10/hr)

Next, is to compare the rates;

For Edge landscaping, we have:

`m = 12.0`

For Gatewood, we have:

`m = 10` ------------ assume the equation is:
`y = 10x + 5`

Compare the rates:

`12 > 10`

Hence, Edge landscaping has a greater hourly rate