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Veronika [31]
3 years ago
10

I need this asap ty:p

Mathematics
2 answers:
Anastasy [175]3 years ago
7 0

Answer:

(a) x = -2y

(c) 3x - 2y = 0

Step-by-step explanation:

You can tell if an equation is a direct variation equation if it can be written in the format y = kx.

Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

(a) x = -2y

  • y = x/-2 → y = -1/2x
  • This is equivalent to multiplying x by -1/2, so this is an example of direct variation.

(b) x + 2y = 12

  • 2y = 12 - x
  • y = 6 - 1/2x
  • This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is <u>NOT</u> an example of direct variation.

(c) 3x - 2y = 0

  • -2y = -3x
  • y = 3/2x
  • This follows the format of y = kx, so it is an example of direct variation.

(d) 5x² + y = 0

  • y = -5x²
  • This is not in the form of y = kx, so it is <u>NOT</u> an example of direct variation.

(e) y = 0.3x + 1.6

  • 1.6 is being added to 0.3x, so it is <u>NOT</u> an example of direct variation.

(f) y - 2 = x

  • y = x + 2
  • 2 is being added to x, so it is <u>NOT</u> an example of direct variation.

The following equations are examples of direct variation:

  • x = -2y
  • 3x - 2y = 0
BlackZzzverrR [31]3 years ago
3 0

Answer:

(a) x = -2y

(c) 3x - 2y = 0

Step-by-step explanation:

You can tell if an equation is a direct variation equation if it can be written in the format y = kx.

Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

(a) x = -2y

y = x/-2 → y = -1/2x

This is equivalent to multiplying x by -1/2, so this is an example of direct variation.

(b) x + 2y = 12

2y = 12 - x

y = 6 - 1/2x

This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is NOT an example of direct variation.

(c) 3x - 2y = 0

-2y = -3x

y = 3/2x

This follows the format of y = kx, so it is an example of direct variation.

(d) 5x² + y = 0

y = -5x²

This is not in the form of y = kx, so it is NOT an example of direct variation.

(e) y = 0.3x + 1.6

1.6 is being added to 0.3x, so it is NOT an example of direct variation.

(f) y - 2 = x

y = x + 2

2 is being added to x, so it is NOT an example of direct variation.

The following equations are examples of direct variation:

x = -2y

3x - 2y = 0

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The very first thing you should do with a question like this is get the graph. Then you will know what you are looking for. I have provided you with such a graph. Your table should center around -2 ≤ x ≤ -1

So let's set up a table and see what we get. Start with y = x + 5

x             x + 5
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-2           3

Do the same thing for - (3)^x + 4 See below to see how this is entered your calculator

x            -(3)^x + 4
-1           3.66
-1.25      3.75
-1.5        3.8
-1.75      3.85
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Conclusion
When x = - 1.25 y = 3.75 for both graphs. <<<< Answer

Footnote
You may not be familiar with how to put this in your calculator. This is the way I would do it. I'm only doing it for y = -(3^x) + 4

Let x = - 1.25
3
^ Note your calculator might have x^y or y^x. You'll have 1 of the three.
1.25
+/- 
=
X
1
+/-
=     At this point you should have -0.25
+
4
= 
That gives you 3.75



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