Question

Finding the Slope and InterceptA 4-column table with 6 rows. Column 1 is labeled x with entries 1.5, 3, 5.5, 6.25, 7, Sigma-summation x almost-equals 23.25. Column 2 is labeled y with entries 9.5, 17, 34.5, 31, 35, sigma-summation y almost-equals 127. Column 3 is labeled x squared with entries 2.25, 9, 30.25, 39.06, 49, sigma-summation x squared almost-equals 129.56. Column 4 is labeled x y with entries 14.25, 51, 189.75, 193.75, 245, sigma-summation x y almost-equals 693.75.The table shows the relationship between the number of trucks filled with mulch (x) and the number of tons of mulch (y) delivered by a landscaping company. Which regression equation models the data?y = 4.8x + 3y = 3x + 4.8y = x + 20.8y = 20.8x + 1

Answer 1

C

Step-by-step explanation:

Answer 2

Step-by-step explanation:

We are given a table of x and y values along with other information that is useful to calculate the regression equation that models the data.

Step 1. The equation will have the following form:

`y=mx+b`

Where m is the slope of the line, and b is the y-intercept of the line.

Step 2. There are two formulas useful to calculate m and b, and they are presented in the following image:

Where the symbol

∑

represents a summation.

The summations are already presented in the table:

We will use the values to substitute in our formulas.

Step 3. In our formulas, there is a value 'n', this value represents the number of elements in the data, in this case, n is equal to 5:

`n=5`

Substituting the values from the table and the value of n to find m:

`m=((5)(693.75)-(23.25)(127))/((5)(129.56)-(23.25^)^2)`

Solving the operations, we find the value of m:

`m=4.8117`

We can round this value to

`m=4.8`

Step 4. We already have m, so now we need to find b:

Substituting the known values:

`b=(127-4.8(23.25))/(5)`

Solving the operations:

`b=3.08`

we can round this to

`b=3`

Step 5. Remember that our equation has the form

`y=mx+b`

The last step is to substitute our m and b values:

`y=4.8x+3`

And we have found the line equation which is the first option.

Answer:

`y=4.8x+3`