You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=3/2x+6. There is a tree in your yard at the point (6,2) each unit bin the coordinate plane represents one foot approximately how far away is the tree from the zip line round your answer to the neerest tenth

distance = 10.2

Step-by-step explanation:

From the question, the equation of the line representing the zip line is y=3/2x+6

Let's assume y = 0

3x = 12

x = 4

y = 12

We will have a coordinate ( 4, 12) and (6 , 2)

Solving this problem will requires us to use the distance formula of point to a line.

distance = sqrt root ( X2 - X1)^2 +(Y2 -Y1)^2

distance = sqrt root ( 2^2 + 10^2)

distance = 10.198

To round your answer to the neerest tenth,

distance = 10.2

The equation is y = $72.99 + $28.45(x - 1), where y is the monthly charge and x is the month in which it is calculated.

Step-by-step explanation:

Step 1; First we need to establish a relation between the difference in costs. For the first month it cost $72.99, during the second month, it costs $101.44 and in the third month, it costs $129.89. Difference in rates

Second months rate - First months rate = $101.44 - $72.99 = $28.45

Third months rate - Second months rate = $129.89 - $101.44 = $28.45.

So for every consecutive month, the charges increase by $28.45

Step 2; Now we develop an equation,

y = $72.99 + $28.45(x - 1), where y is the charge that month and x is the month in which it is calculated.

For x = 1, y = $72.99 + $28.45(1 - 1) = $72.99 + $28.45(0) = $72.99,

For x = 2, y = $72.99 + $28.45(x - 1) = $72.99 + $28.45(2 - 1) = $101.44,

For x = 3, y = $72.99 + $28.45(3 - 1) = $72.99 + $28.45(3-1) = $129.89.

So this is the equation to calculate the cost y the mobile provider charges in month x.