Answer:
Part a) [tex]y=0.05x+1.50[/tex]
Part b) [tex]y=0.50x+0.50[/tex]
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
[tex]y=mx+b[/tex]
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
[tex]m=\$0.05\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$1.50[/tex]
substitute
[tex]y=0.05x+1.50[/tex]
Part b)
At gas station store
we have that
The slope or unit rate is equal to
[tex]m=\$0.50\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$0.50[/tex]
substitute
[tex]y=0.50x+0.50[/tex]
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
[tex]y=0.05x+1.50[/tex]
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
[tex]0=0.05x+1.50[/tex]
[tex]x=-30[/tex]
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
[tex]y=0.50x+0.50[/tex]
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
[tex]0=0.50x+0.50[/tex]
[tex]x=-1[/tex]
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
[tex]\$0.05\ per\ refill < \$0.50\ per\ refill[/tex]
The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store
[tex]\$1.50 > \$0.50[/tex]
