You and your friend leave your houses at the same time to meet at a restaurant. the distance (in miles) your friend is from the restaurant is given by y=−40x+100, where x is the number of hours since your friend left home. you live 150 miles from the restaurant and arrive at the same time as your friend. write a linear equation that represents your distance from the restaurant.

  y = - 60 x +150

Step-by-step explanation:

Here, the function which represents the distance between my friend and restaurant,

y = - 40x +100

Where,  x is the number of hours since my friend left home.

Since, when he covered the whole distance y = 0

Then -40x +100 = 0

⇒ -40x  = -100

⇒ x = 2.5

Thus, he is taking 2.5 hours to covered the whole distance.

And, According to question, me and my friend take the same time to covered the distance.

Thus, the time taken by me to covered 150 miles distance = 2.5 hours.

Therefore, my speed = 150/2.5 = 60 miles per hour.

Thus, in x hour the distance between me and restaurant,

y = 150 - 60x

Which is the required equation.

The linear equation that represents my distance from the restaurant is

y = 150 - 60x.

Given data:

The distance between the friends and restaurant is, y = -40x + 100

Here, x is the time function. ( number of hours since your friend left home)

Since, when he covered the whole distance y = 0.

Substituting the value in the equation as,

-40x +100 = 0

-40x  =  -100

x = 2.5

Thus, the friend is taking 2.5 hours to covered the whole distance.

Also time taken by each person is same. Which means  the time taken by me to covered 150 miles distance = 2.5 hours.

Therefore, the speed is calculated as,

Thus, in x hour the distance between me and restaurant is represented by the equation as,

y = 150 - 60x

This is the required equation.

Learn more about the linear equation here:

link

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x