Question

You are flying a kite. You pull in the kite at a rate of 1.75 feet per second. After 8 seconds, the kite is 30 feet from your hands. Write an equation that represents the distance y (in feet) that the kite is from the end of your hands after x seconds. Then graph the equation.

Answer 1

Part 1) the linear equation is
`y=1.75x+16`

Part 2) The graph in the attached figure

Explanation:

Part 1) Write an equation

Let

x ----> the time in seconds

y ----> the distance in feet that the kite is from the end of your hands

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem

we have

`m=1.75\ (ft)/(sec)`

`point\ (8,30)`

substitute

`30=1.75(8)+b`

solve for b

`30=14+b`

`b=30-14`

`b=16\ ft` ----> the initial distance

therefore

The linear equation is equal to

`y=1.75x+16`

Part 2) Graph the equation

we have

`y=1.75x+16`

To graph the line we need two points

we have

(0,16) and (8,30)

Plot the points and connect them to graph the line

Remember that the values of x and y cannot be a negative number

The graph in the attached figure