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
Bas_tet [7]
3 years ago
8

X y

Mathematics
1 answer:
Darina [25.2K]3 years ago
8 0

Answer:

Part 1) The rate of change is \frac{17}{15}

Part 2) The initial value is 68

Part 3) The function rule to the linear model is y=\frac{17}{15}x+68

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

step 1

Find the slope

take two points from the table

(0,68) and (15,85)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{85-68}{15-0}

m=\frac{17}{15}

In a linear function , the slope is the same that the rate of change

therefore

The rate of change is \frac{17}{15}

step 2

Find the y-intercept

we know that

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

Looking at the table

For x=0, y=68

therefore

The y-intercept is

b=68

The y-intercept is also called the initial value

therefore

The initial value is 68

step 3

Determine the function rule to the linear model

y=mx+b

we have

m=\frac{17}{15}

b=68

substitute

y=\frac{17}{15}x+68

You might be interested in
1. Write the equation in standard form. Identify the important features of the graph:
NeTakaya

Answer:

  1. (x-4.5)^2 +(y +5)^2 = 30.25
  2. x = (1/8)y^2 +(1/2)y +(1/2)
  3. y^2/36 -x^2/64 = 1
  4. x^2/16 +y^2/25 = 1

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

  (x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

  (x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

__

2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

  x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

__

3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

  y^2/36 -x^2/64 = 1

__

4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

  x^2/16 +b^2/25 = 1

_____

The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

6 0
3 years ago
Determine the gradient of the straight line 2x-3y+9=0. Find the equation of the straight line through the origin which is perpen
frutty [35]

Answer: 3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line  

a

x

+

b

y

+

c

=

0

is  

m

=

−

a

b

∴

The slope of the line  

2

x

+

3

y

=

9

is  

m

1

=

−

2

3

∴

The slope of the line perpendicular to  

2

x

+

3

y

=

9

is  

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through  

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

x

1

)3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line  

a

x

+

b

y

+

c

=

0

is  

m

=

−

a

b

∴

The slope of the line  

2

x

+

3

y

=

9

is  

m

1

=

−

2

3

∴

The slope of the line perpendicular to  

2

x

+

3

y

=

9

is  

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through  

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

Explanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m  

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute  

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular lineExplanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m  

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute  

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular line

7 0
3 years ago
Read 2 more answers
Your class is taking a trip to a museum that is 190 miles away. The bus can travel at 55 miles per hour. At least how many hours
Fofino [41]

Answer:

3 hours and 45 minutes

Step-by-step explanation:

190/55=3.4545

8 0
3 years ago
Cost of 5 m ribbon = 7.5 and cost of 1 m ribbon is​
Umnica [9.8K]

Answer:

1.50

Step-by-step explanation:

7.5 is <em>1.5</em><em> </em><em>x</em><em> </em>5 so, 1 x 1.5 = 1.5

5 0
3 years ago
Antonio gave 27 tomatoes to his neighbor and 15 to his brother. he had72 tomatoes before giving some away. how many tomatoes doe
SVETLANKA909090 [29]
At first he had 72 then he gave 27 to his neighbor  ( 27 subtract 72 = 45) and then he gave 15 to his brother  ( 45 subtract 15 = 30) 

he had 30 tomatoes left.
                                                                               
6 0
3 years ago
Other questions:
  • suppose y varies directly with x, and y = 8 when x = -6. what direct variation equation relates x and y? what is the value of y
    5·1 answer
  • 2 times the quantity 3 times c plus 9
    15·1 answer
  • Draw a model on grid paper to find the product of 3 and 1.4. What is the product?
    5·1 answer
  • Z + 21/–1 = –3. z+21/-1 is a fraction
    13·2 answers
  • Pls help I forgot how this works
    6·1 answer
  • Solve for y from the standard form<br> 3x - 8y = 24
    15·2 answers
  • Plzz help will help you if i can!!!!! How does a house cat exhibit the seven characteristics of life?
    8·2 answers
  • Kim was asked to explain to her friends how to solve 3x? - 2x = 1. She will be using the quadratic formula. What would be the fi
    5·1 answer
  • I am horrible with these problems!
    10·1 answer
  • [Maximum mark: 6]
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!