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Stolb23 [73]
3 years ago
9

How would the graph of the relation y=3x-2 change if the 3 and -2 were both doubled? 

Mathematics
1 answer:
Lena [83]3 years ago
6 0
<u>y = 3x - 2</u>

-- The ' 3 ' is the slope. If you double it to ' 6 ', the line is steeper.

-- The ' -2 ' is the y-intercept. If you double it to ' -4 ', the line crosses the y-axis lower.

Choice <u>(a)</u> says that . . . "... steeper, and lower y-intercept".

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What is the equation of the line that is perpendicular to y=2/3x-5 and passes through (6,-1)?
riadik2000 [5.3K]

Answer: 2y + 3x - 16 = 0

Step-by-step explanation:

Equation of the line  is    y = 2x/3 - 5

From the equation , the slope m₁ = 2/3. therefore recall, from condition for perpendicularity, m₁m₂ = -1

The product of their gradient must be (-1).

Now since m₁ = 2/3 and m₁m₂ =-1

                          2m₂/3 = -1

Therefore , m₂ = -3/2.

Since the equation passes through the coordinate of (6,-1)

we now substitute for x and y in the equation of a line to get the y intercept (c)

  y = mx + c

  -1 = -3x/2 +c

  -1 = -3/2 x 6 + c

  -1 = -9 + c

  -1 + 9 = c

 Therefore c = 8

Now to get the equation of line that is perpendicular to y = 2x/3 - 5

 y = -3x/2 + 8

making it a linear equation,

 2y = -3x + 16

 2y +3x - 16 = 0

6 0
3 years ago
Which expression is equivalent to [(3xy^-5)^3 / (x^-2y^2)^-4]^-2
True [87]
<span>The answer is (x</span>¹⁰<span>y</span>¹⁴<span>)/729.

Explanation:
We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us

[(3</span>³<span>x</span>³<span>y</span>⁻¹⁵<span>)/(x</span>⁸<span>y</span>⁻⁸<span>)]</span>⁻²<span>.

Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have
[(3</span>³<span>x</span>³<span>y</span>⁸<span>)/(x</span>⁸<span>y</span>¹⁵<span>)]</span>⁻²<span>.

Using the quotient property, we subtract exponents when dividing powers, which gives us
(3</span>³<span>/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Evaluating 3</span>³<span>, we have
(27/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Using the power of a power property again, we have
27</span>⁻²<span>/x</span>⁻¹⁰<span>y</span>⁻¹⁴<span>.

Flipping the negative exponents again gives us x</span>¹⁰<span>y</span>¹⁴<span>/729.</span>
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