Question

A restaurant sells tea for $1.50 plus $0.05 per refill a gas station store sells tea for $0.50 plus $0.50 per refill?

Answer 1

Part a)
`y=0.05x+1.50`

Part b)
`y=0.50x+0.50`

Part c) The graph in the attached figure

Part d) see the explanation

Explanation:

The complete question is

A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.

Part a) Write a linear function for the price of tea at restaurant

Part b) Write a linear function for the price of tea at gas station store

Part c) Graph both equations

Part c) Compare the lines in terms of slope and y-intercept

Let

y -----> the price of tea in dollars

x -----> the number of refills

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 (value of y when the value o x is equal to zero)

Part a)

At restaurant

we have that

The slope or unit rate is equal to

`m=\$0.05\ per\ refill`

The initial value or y-intercept is equal to

`b=\$1.50`

substitute

`y=0.05x+1.50`

Part b)

At gas station store

we have that

The slope or unit rate is equal to

`m=\$0.50\ per\ refill`

The initial value or y-intercept is equal to

`b=\$0.50`

substitute

`y=0.50x+0.50`

Part c) Graph both equations

we know that

The easiest way to graph a line is with two points

Find the intercepts of the line

At restaurant

`y=0.05x+1.50`

The y-intercept is the point (0,1.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

`0=0.05x+1.50`

`x=-30`

The x-intercept is the point (-30,0)

Plot the points and join to graph the line

see the attached figure

At gas station store

`y=0.50x+0.50`

The y-intercept is the point (0,0.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

`0=0.50x+0.50`

`x=-1`

The x-intercept is the point (-1,0)

Plot the points and join to graph the line

see the attached figure

Part c) Compare the lines in terms of slope and y-intercept

The slope or unit rate at the restaurant is less than the slope at the gas station store

`\$0.05\ per\ refill < \$0.50\ per\ refill`

The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store

`\$1.50 > \$0.50`