Find an equation of the line through (3,5) and parallel to y = 3x -7. Write the equation using function notation
f(x)=__​

Answers

Answer 1

Given:

Equation of line is [tex]y=3x-7[/tex].

To find:

The equation of line which is parallel line to [tex]y=3x-7[/tex] and passes through (3,5) in function notation.

Solution:

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

On comparing the equation [tex]y=3x-7[/tex] with slope intercept form, we get

[tex]m=3[/tex]

So, slope of given line is 3.

Slope of parallel lines are same. Thus, the slope of parallel line is also 3.

Point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

where, m is slope.

The parallel line passes through (3,5) with slope 3. So, the equation of line is

[tex]y-5=3(x-3)[/tex]

[tex]y-5=3x-9[/tex]

Add 5 on both sides.

[tex]y=3x-9+5[/tex]

[tex]y=3x-4[/tex]

Function notation of this equation is

[tex]f(x)=3x-4[/tex]

Therefore, the equation equation in function notation is [tex]f(x)=3x-4[/tex].


Related Questions

Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sister who is two years younger than him. If the product of his sisters' ages is 70, how old is Richard?

Answers

Answer:

7 years

Step-by-step explanation:

Given that:

Let Richard's age = x

Elder sister's age = 2x

Youngwr sister's age = x - 2

Product of sisters ages = 70

2x * (x - 2) = 70

2x² - 4x = 70

2x² - 4x - 70 = 0

x² - 2x - 35 = 0

x² - 7x + 5x - 35 = 0

x(x - 7) +5(x - 7) = 0

(x - 7) or (x + 5) = 0

x = 7 or x = - 5

X can't be negative

Hence, x = 7

Richard is 7 years

The members of a crew team can weigh no more than 165 pounds each. Write an INEQUALITY for the acceptable weights. Graph the solutions.

Answers

Answer:

shut up b

sorry gad will elp you

Step-by-step explanation:

PLZ HELP ASAP 30 POINTS!!! write the equation of the line in standard form and slope-interpret form.
standard form:
slope-interpret form:

Answers

standard form: 3x-y= -3
slope intercept: 3x + 3

Delta owns a D.C. 10 airplane that has seats for 318 people. The company flies this airplane only if there are at least 96 people on the plane. Write a compound inequality to show the possible number of people on a Delta flight. Let n represent the amount of people.

Answers

Answer: n greater than or equal to 96 or n is greater than or less than 318

Step-by-step explanation:

Brainliest plz

POINTS plus will mark BRAINLIEST for the correct answer

Answers

Answer:

I believe the answer is 9

Step-by-step explanation:

The most balloons she has is 180 and she can make 20 animals with that so 180/20=9

The answer to your question is 9

How do I solve 4x+23>-21

Answers

Answer:

Inequality Form:

x>-11

Step-by-step explanation:

Interval Notation:

(-11,\infty )

Answer:

Step-by-step explanation:

4x + 23 > -21

4x > -21 -23  (moving 23 to the right side of equation changes the +23 to  -23

4x > -44  (adding -21 to -23)

x > -11  (dividing both sides of equation by 4, this keeps the equation the same

Solution:  x > -11  (x is greater than negative 11)

PLEASE HELP!!Choose the slope and y-intercept that
correspond with the graph.

Answers

the answer is -1/3 y-incercept= -1

Answer:

The first one

Step-by-step explanation:

It’s y intercept is 1 and the slope is 1/3 because it goes up one and to the left 3 . I know it’s negative because it’s going down to the right.

A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a
predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?

Answers

Answer: 7 meters

Step by step explanation:

Now write an equation that represents the situation. You want to find the change in the dolphins depth, so subtract it’s beginning depth from its final depth.


Hope it helps!

Please help me answer 16 please

Answers

Answer:

SSS

Step-by-step explanation:

I can identify that these triangles are congruent by using the SSS (Side, Side, Side) postulate theorem. I know this because first, second, and home triangle share the same side as the third, second, and home triangle, meaning they are congruent, so are the other sides of the angle since the question states they are congruent.

Write the equation of the line, in point slope form that goes through the given point with the given slope. through: (-2,5), slope = -4* O y + 2 = 5(x + 4) O y - 2 = 5(x-4) O y + 5 = -4(x +2) O y- 5 = -4(x + 2)​

Answers

Answer:

y-5 = -4(x + 2)

Step-by-step explanation:

The point slope form is;

y-y1 = m(x-x1)

where m represents the slope

(x1, y1) represents the given point

Thus;

y-5 = -4(x + 2)

simplefy the equation

Answers

Answer:

i wish i could simply life.

Step-by-step explanation:

What is the nth term rule of the quadratic sequence below?
-5, -3,3, 13, 27, 45, 67, ...

Answers

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

Answer:

[tex]u_{n} = 2n^{2} -4n-3[/tex]

Step-by-step explanation:

a +b + c = - 5    First term in sequence

3a + b = 2   Difference between first two terms

2a = 4         Difference between  the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so  b = -4; 2 - 4 + c = -5  → -2 + c = -5 so c = -3

[tex]-0.2\sqrt{x^2}[/tex] You have to simplify this

Answers

Answer:

The simplified answer to that is -0.2x.

Hope this helps and if you could mark this as brainliest. Thanks!

Answer:

-0.2x

Step-by-step explanation:

If x is negative then,

-0.2(-2) = 0.4

Chloe drives from her house to her Grandma's house 48 miles away in an hour and 12 minutes. How far could she travel in 9 minutes?
a.12 miles
b.6 miles
c.8 miles
d.24 miles

Answers

Answer:

B. 6 miles

Step-by-step explanation:

first you convert the hour and 12 minutes into only minutes

72 minutes

then you set up in a fraction

48/72 = x/9

then solve for x, if you use a calculator it will give you 6

No texto Nascimento do Queijo,qual das crianças criou a teoria mais distante da realidade?

Answers

Answer:

ejre' fe trerxto fno

Step-by-step explanation:

A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60
kilometers from the runway. What is the angle of depression for the descent of the plane?
Round to the nearest degree.

Answers

Answer:

Angle of depression = 3.37°

Step-by-step explanation:

We are told that A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60

kilometers from the runway.

I've attached an image of a triangle depicting this question.

From the triangle, we can find the angle of depression θ from trigonometric ratio since it's a right angle triangle.

Thus;

3.5/60 = tan θ

tan θ = 0.0583

θ = tan^(-1) 0.0583

θ = 3.37°

Solve this equation.

23x−15x=x−1

Answers

Answer:

x = -1/7

Step-by-step explanation:

25x - 15x = x - 1

combine like terms

7x = -1

divide

x = -1/7

Answer:

x = -1/7 (the whole fraction is negative)

Step-by-step explanation:

23x−15x=x−1

8x = x - 1

8x - x = x - 1 - x

7x = -1

x = -1/7

Help will give a crown!!

Answers

Answer:

okay

Step-by-step explanation:

1) Each side length is 12

2) Each side length is 2


What is the slope of a line that is perpendicular to a line that has a slope of -7

Please help ya girl out :))

Answers

C. 1/7
The slope of a perpendicular line will be the opposite of the first slope given. So since the first slope is -7 then we make the negative positive and flip the numerator and denominator. So -7/1 will be 1/7

y = (x - 4)(x-8)
Distribution

Answers

Answer:

[tex]y= x^{2} -12x+32[/tex]

Explanation:

[tex]y=x^{2} -8x-4x+32\\y= x^{2} -12x+32[/tex]

where is plymoth rock

Answers

Answer:

If u mean plymouth rock then the answer is

Lost at sea, they happened upon a piece of land that would become known as Cape Cod. After surveying the land, they set up camp not too far from Plymouth Rock. ... The 102 travellers aboard the Mayflower landed upon the shores of Plymouth in 1620. This rock still sits on those shores to commemorate the historic event.

Step-by-step explanation:

Plz help...kinda confused.....only answer if ya know....:)
-3=-v+7
v=​

Answers

Answer:

-3 = -v + 7

-3 - 7 = -v

3+7 = -v

-10 = -v

10 = v

Step-by-step explanation:

this is the answer i got, using basic algebra...

i hope this helps....

have a great day ahead :)

Answer:

v = 10

Step-by-step explanation:

[tex]-3=-v+7\\\\-v+7=-3\\\\-v+7-7=-3-7\\\\-v=-10\\\\\frac{-v=-10}{-1}\\\\ \boxed{v=10}[/tex]

Hope this helps.

entlying
A and B are forces acting on a falling object. Which
force, A or B, represents gravity in the diagram?
Force
is gravity because it attracts the ball
to the ground.

Answers

Answer:

B... Because indicates the direction of gravity because its direction is downward

Answer:b

Step-by-step explanation:

a rental car company charges a customer $60 plus $0.32 per mile. write the equation that best describes the relationship between the cost, y, of renting the car and the number of miles, x, the car was driven​

Answers

Answer:

0.32x + 60= y

Step-by-step explanation:

what the slope of (15,9) (-10,3) ​​

Answers

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[tex]slope = \frac{3 - 9}{ - 10 - 15} \\ [/tex]

[tex]slope = \frac{ - 6}{ - 25} \\ [/tex]

[tex]slope = \frac{6}{25} \\ [/tex]

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Answer:

The slope is [tex]\frac{6}{25}[/tex] or [tex]0.24[/tex].

Step-by-step explanation:

This is the formula to calculate the slope from two given points: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] . Now, substitute (x1, y1) and (x2, y2) for (15,9) and (-10,3). [tex]slope=\frac{3-9}{-10-15}[/tex] . That equation becomes [tex]slope=\frac{-6}{-25}[/tex] . You have to change [tex]\frac{-6}{-25}[/tex] to [tex]\frac{6}{25}[/tex] . The slope is 6/25 or in decimal form, 0.24.

Which exponential function is represented by the graph?
O f(x) = 2( 1/2 )x
O f(x) = 1/2(2)x
O f(x) = 1/2(1/2)x
Of(x) = 2(2)x
PLEASE HELP MEE!

Answers

Answer:

f(x) = [tex]\frac{1}{2}[/tex] [tex](2)^{x}[/tex]

Step-by-step explanation:

Using the standard form of the exponential function

y = a [tex]b^{x}[/tex]

To find a and b , substitute ordered pairs from the graph

Using (0, 0.5 ), then

0.5 = a[tex]b^{0}[/tex] [

a = 0.5 , so

y = [tex]\frac{1}{2}[/tex] [tex]b^{x}[/tex]

Using (1, 1) , then

1 = [tex]\frac{1}{2}[/tex][tex]b^{1}[/tex] , thus

b = 2

f(x) = [tex]\frac{1}{2}[/tex][tex](2)^{x}[/tex] ← exponential function representing graph

Will mark brainliest! Please help I have no idea!

Answers

Answer:

the decimals should line up.

Answer:

press the right arrow 3 times

Step-by-step explanation:

to properly subtract any numbers the value of the digits need to be in line

Help me please. I’m trying very hard.

Answers

Answer:

27/3

Step-by-step explanation:

50-(18+5)= 27

27/3

Need Answer ASAP only 5 min

Answers

70 mb is the answer

Answer: 70

Step-by-step explanation:

1. Divide 528 by 264 to get 2

2. Do 2 times 35 to get 70

You are tasked with buying pizza for a party that has 100 guests. 40 guests are children, and 60 guests are adults. Half of the children want pizza, and two thirds of the adults want pizza. Children will eat one slice of pizza, and adults will eat two slices of pizza. A pizza pie can be cut into 8 slices and costs $9 dollars per pie.

Answers

Total slices required for children,

[tex]C = \dfrac{40}{2}\times 1\\\\C = 20\ slices[/tex] .

Total slices required for adults,

[tex]A=\dfrac{2}{3}\times 60\times 2\\\\A = 80\ slices[/tex]

So, total slices required are, 20 + 80 = 100 .

Number of pizza, n = 100/8 = 12.5

So, he has to order 13 pizza cause pizza cannot be purchased in fraction.

Total price, P = 13 × 9 = $117 .

Hence, this is the required solution.

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