What is the equation of the line?

Mathematics

1 answer:

andrew11 [14]3 years ago

5 0

Your answer is y = 1/2x + 2. The slope formula is y = mx + b. To find the y-intercept, (b) you just look at where the line intercepts on the y-axis, which in your case it intersects at positive two. You can find the slope by using the rise over run formula. To get from point A to point B, the line rises up one on the graph, and "runs" over two, so the slope would be 1/2. Then we plug these numbers into the formula to get y = 1/2x + 2.

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Answer:

$\dfrac{y^{18}}{8x^{18}}$

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

a^-b = 1/a^b

(a^b)^c = a^(bc)

Your expression simplifies as follows:

$\left(\dfrac{10x^3y^{-2}}{5x^{-3}y^4}\right)^{-3}=(2x^{3-(-3)}y^{-2-4})^{-3}=(2x^6y^{-6})^{-3}\\\\=(2^{-3})x^{6(-3)}y^{(-6)(-3)}=\dfrac{1}{8}x^{-18}y^{18}\\\\=\boxed{\dfrac{y^{18}}{8x^{18}}}$