Arestaurant 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)

Part b)

Part c) The graph in the attached figure

Part d) see the explanation

Step-by-step 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

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

The initial value or y-intercept is equal to

substitute

Part b)

At gas station store

we have that

The slope or unit rate is equal to

The initial value or y-intercept is equal to

substitute

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

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

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

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

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

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

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w