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kodGreya [7K]
3 years ago
6

Which equation represents a linear function?

Mathematics
1 answer:
Mila [183]3 years ago
6 0

The equation y - 2 = -5(x - 2) represents a linear function ⇒ 1st answer

Step-by-step explanation:

A linear function is any function that graphs to a straight line

(not a vertical line)

The forms of the linear equation are

  • y = m x + b, where m is the slope of the line which represents the function and b is the y-intercept ⇒ slope-intercept form
  • y-y_{1}=m(x-x_{1}), where m is the slope and (x_{1},y_{1}) is a point lies on the line which represent the function ⇒ slope-point form
  • Ax + By = C, where A, B, and C are constant ⇒ standard form

Linear function means the greatest power x and y in the equation of the function is 1

∵ The equation is y - 2 = -5(x - 2)

∵ The greatest power of x and y is 1

∵ The equation is in the form of y-y_{1}=m(x-x_{1}), where

   m = -5 and the coordinates of the point are (2 , 2)

∴ The equation represents a linear function

The equation y - 2 = -5(x - 2) represents a linear function

Learn more:

You can learn more about the linear function in brainly.com/question/4326955

#LearnwithBrainly

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Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”
Leviafan [203]

Answer:

The equation determine a relation between x and y

x = ± \sqrt{1-(y-2)^{2}}

y = ± \sqrt{1-x^{2}}+2

The domain is 1 ≤ y ≤ 3

The domain is -1 ≤ x ≤ 1

The graphs of these two function are half circle with center (0 , 2)

All of the points on the circle that have distance 1 from point (0 , 2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation x² + (y - 2)² and the relation "(x , y) R (0, 2)", where

 R is read as "has distance 1 of"

- This relation can also be read as “the point (x, y) is on the circle

 of radius 1 with center (0, 2)”

- “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”

* <em>Lets solve the problem</em>

- The equation of a circle of center (h , k) and radius r is

  (x - h)² + (y - k)² = r²

∵ The center of the circle is (0 , 2)

∴ h = 0 and k = 2

∵ The radius is 1

∴ r = 1

∴ The equation is ⇒  (x - 0)² + (y - 2)² = 1²

∴ The equation is ⇒ x² + (y - 2)² = 1

∵ A circle represents the graph of a relation

∴ The equation determine a relation between x and y

* Lets prove that x=g(y)

- To do that find x in terms of y by separate x in side and all other

  in the other side

∵ x² + (y - 2)² = 1

- Subtract (y - 2)² from both sides

∴ x² = 1 - (y - 2)²

- Take square root for both sides

∴ x = ± \sqrt{1-(y-2)^{2}}

∴ x = g(y)

* Lets prove that y=h(x)

- To do that find y in terms of x by separate y in side and all other

  in the other side

∵ x² + (y - 2)² = 1

- Subtract x² from both sides

∴ (y - 2)² = 1 - x²

- Take square root for both sides

∴ y - 2 = ± \sqrt{1-x^{2}}

- Add 2 for both sides

∴ y = ± \sqrt{1-x^{2}}+2

∴ y = h(x)

- In the function x = ± \sqrt{1-(y-2)^{2}}

∵ \sqrt{1-(y-2)^{2}} ≥ 0

∴ 1 - (y - 2)² ≥ 0

- Add (y - 2)² to both sides

∴ 1 ≥ (y - 2)²

- Take √ for both sides

∴ 1 ≥ y - 2 ≥ -1

- Add 2 for both sides

∴ 3 ≥ y ≥ 1

∴ The domain is 1 ≤ y ≤ 3

- In the function y = ± \sqrt{1-x^{2}}+2

∵ \sqrt{1-x^{2}} ≥ 0

∴ 1 - x² ≥ 0

- Add x² for both sides

∴ 1 ≥ x²

- Take √ for both sides

∴ 1 ≥ x ≥ -1

∴ The domain is -1 ≤ x ≤ 1

* The graphs of these two function are half circle with center (0 , 2)

* All of the points on the circle that have distance 1 from point (0 , 2)

8 0
3 years ago
P − 6 = −5 pls help meeee
ExtremeBDS [4]

Answer:

p−6=−5

Add 6 to both sides.

p−6+6=−5+6

p=1

I hope it helps.

5 0
3 years ago
Calculate the slope of the line (-6,-3) (-2,-3)
Vika [28.1K]

Answer:

There is no slope

Step-by-step explanation:

When finding the slope both numbers have to be positive without positive numbers you will not have a positive slope there fore no slope

4 0
2 years ago
F(x) = 3x + 8; g(x) = 5x - 9<br> (a) Find (f + g)(x).
AysviL [449]

Answer: f(x) = 8x -1

Step-by-step explanation:

( f + g )x = 3x + 5x + 8 - 9

( f + g)x = 8x - 1

8 0
3 years ago
Scarlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
Crazy boy [7]
It's directly proportional, so
m=kw

Find the value of k
900=k(18)
k= 50

Answer: m=50w
6 0
3 years ago
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