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
Andrei [34K]
3 years ago
7

Write the rule for the linear function. Remember a function rule is written using f(x)

Mathematics
1 answer:
Marina CMI [18]3 years ago
4 0

Answer:

The rule for the linear function will be:

f(x) = -2x+5

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

  • (1, 3)
  • (2, 1)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)

m=\frac{1-3}{2-1}

m=-2

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

y-y_1=m\left(x-x_1\right)

y - 3 = -2 (x-1)

y-3 = -2x+2

adding 3 to both sides

y-3+3 = -2x+2+3

y = -2x+5

or

f(x) = -2x+5

Therefore, the rule for the linear function will be:

f(x) = -2x+5

You might be interested in
What is the last number in the number sequence given below? 10 : 10 : 20 : 45 : 110 : 300 : ?
MrRissso [65]
To get from the first number to the second number the equation is 10x0.5+5=10
Thereafter the equation to get to the next number is 10x1.0+10=20
Thereafter the equation to get the next number is 20x1.5+15=45
Thereafter the equation to get the next number is 45x2.0+20=110
You can notice the pattern, the first number is what the last number was, you increase the second number by 0.5 and you increase the third number by 5.
Following this pattern to find the last number you do 110x2.5+25. This equation results in the number 300. Now time for the last number. You input 300x3.0+30. The answer results in 930. Therefore, the missing number is 930. 
3 0
3 years ago
Read 2 more answers
Kai has been saving up money to buy a new backpack that is originally priced at $88.95. The store is having a 40% off end of sea
Fiesta28 [93]

Answer:

yes, he can but the backpack.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A jar contains six blue marbles and five red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you ch
TEA [102]

The jar has 6+5=11 marbles.

We have to find the probability of the following event:

1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red

2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)

The probability of the first event is:

P_1=\frac{5}{11}

The probability of the second event is:

P_2=\frac{4}{10}=\frac{2}{5}

The probability of the both events to happen is:

P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818

3 0
3 years ago
Mrs. Nally's swimming pool is 10 feet by 6 feet. She paves the area around it with a sidewalk x feet wide, using 80 square feet
andrew11 [14]

Answer:

The sidewalk is 2 feet wide

Step-by-step explanation:

The area of the sidewalk is given as 80 square feet

The length and width of pool

including side walks will be;

10 + 2x and 6 + 2x

To get the area of the side walk

That will be area of total minus area of the pool

That will be ;

(10 + 2x)(6 + 2x) - 10(6) = 80

60 + 12x + 20x + 4x^2 - 60 = 80

4x^2 + 32x -80 = 0

x^2 + 8x -20

x^2 + 10x - 2x - 20 = 0

x(x + 10) -2(x + 10) = 0

(x-2)(x + 10) = 0

x = 2 or -10

since width cannot be negative;

The sidewalk is 2 feet wide

6 0
3 years ago
GIVING 25 POINTS:
nignag [31]

Answer:

A Sarah earns more money per hour  $15

Step-by-step explanation:

We need to find the slope to determine the rate ( amount per hour

Sarah

m = (y2-y1)/(x2-x1)

    = (50-5)/(3-0)

    = 45/3

    = $15 per hour

Mia

m = (y2-y1)/(x2-x1)

   = (20-10)/(2-0)

    = 10/2

   = $5 per hour

6 0
3 years ago
Read 2 more answers
Other questions:
  • A scientist uses a submarine to study ocean life. She begins at sea level, which is at an elevation of 0 feet She travels straig
    7·1 answer
  • Yasmine made waffles for her family.4/7 of the waffles where blueberry 1/7 of the waffles where chocolate chip . The rest of the
    6·1 answer
  • Meg pounded a stake into the ground. When she
    5·1 answer
  • Which measure is greater six feet or two meters
    5·1 answer
  • Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
    9·1 answer
  • A set of data has been organized using the stem-and-leaf plot below. What is the range of the data?
    13·1 answer
  • PLEASE HELP <br> I don’t understand <br> DONT USE ME FOR POINTS
    15·1 answer
  • What is the equation of the line in slope-intercept form?
    8·1 answer
  • Can someone please help me
    13·2 answers
  • Quadrilateral ABCD is transformed to create A′B′C′D′. Match the coordinates of A′ with the transformations that create it.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!