1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KengaRu [80]
3 years ago
14

Melissa frosted some cupcakes in the morning for a party. the table shows the total number of cupcakes frosted after she starts

up after lunch. assume the relationship between the two quantities is linear. find and interpret the rate of change and the initial value.

Mathematics
1 answer:
makvit [3.9K]3 years ago
3 0
Answer:
rate of change = 4/5 = 0.8
initial value = 24

Explanation:
Part (1): getting the rate of change:
The rate of change means the change of the output with respect to the change in the input.
Since we are given that the relation is linear, therefore, the rate of change is constant at any point that belongs.
First, we will need to choose any points from the table. I will choose points : (5,28) and (15,36)
The rate of change is also known as the slope of the line and can be calculated using the following rule:
rate of change = slope of line = (y2-y1) / (x2-x1)
Substitute with the points you chose to get the rate of change as follows:
rate of change = (36-28) / (15-5) = 4/5 = 0.8

Part (2): getting the initial value:
The initial value is defined as the output when the input is zero. Therefore, it is the value of the "y" when the value of the "x" is zero.
The general form of the linear is function is:
y = mx + c
where:
m is the slope
c is the y-intercept
We have the slope = 4/5
Therefore, equation of the line now is:
y = (4/5) x + c
Now, we need to get the y-intercept. To do so, we will use any point that belongs to the function to substitute in the equation and then solve for c. I will choose point (20,40)
y = (4/5) x + c
40 = (4/5)(20) + c
c = 40-16 = 24
Therefore, the equation of the line now becomes:
y = (4/5)x + 24
Now, to get the value, we will substitute the x with zero and get the corresponding y as follows:
y = (4/5)x + 24
y = (4/5)(0) + 24
initial value of y = 24

Hope this helps :)
You might be interested in
Simplify the given expression. Write your answer with positive exponents.
irina [24]

Answer:

heres your answer

Step-by-step explanation:

here you go miss.

4 0
2 years ago
Help plz show all your steps
Elena L [17]

Answer:

$15.5

Step-by-step explanation:

33.50-18=15.5

jope it helps ypu a lot.

7 0
2 years ago
Helppp fast (picture)
harkovskaia [24]
The answer to your question is the first option! Hope this helps. God bless
4 0
3 years ago
Which property allows you to write the expression
umka2103 [35]

Answer:

the associative property

Step-by-step explanation:

the associative property allows the numbers to add regardless of how you group the numbers

8 0
3 years ago
Help needed plaese✌​
monitta

5x-3=2.5x+x solve this equation that I just gave you for X then plug it in to 2.5x and that will equal MN

7 0
3 years ago
Other questions:
  • A study uses a sample of 200 college students to learn about the number of hours they studied for their final exams. The mean nu
    15·2 answers
  • Two competing gyms each Two competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcar
    8·2 answers
  • How can you manipulate |(3-X)| to |(X-3)| ?
    11·1 answer
  • Find -3\7 ÷ -1 1\14
    14·2 answers
  • A rock climber is climbing up a 450 feet high
    10·1 answer
  • Can someone please help me
    5·1 answer
  • I need help with this
    14·2 answers
  • Tracy has 7/8 pounds of butter in her refrigirator. She uses 2/3 of it for cookie batter. How much of the butter did she use?
    13·1 answer
  • Tyrone is twice as old as his daughter. In six years Tyrone's age will be
    5·1 answer
  • HELP PLS o 9 10 11 Are the triangles below acute, obtuse, or right? Triangle A Triangle B Triangle C Triangle D 55 80° 600 35 11
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!