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3 years ago

What is the slope of a line that is perpendicular to the line whose equation is 3x+2y=6?

Mathematics

2 answers:

LekaFEV [45]3 years ago

7 0

first, we can find the slope from the equation that is given buy solving the equation for y

3x+2y = 6

2y = 6-3x

y = 3-3/2x

y = -3/2x+3

now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2

perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have

-3/2 → 3/2 → 2/3

the slope of the perpendicular line is 2/3

hope this helped

Mashcka [7]3 years ago

7 0

Since this equation is already in standard form, there is no need to convert it. Standard form is Ax + By = C. In this equation, 3 = A, 2 = B, and 6 = C. From standard form, Ax + By = C equals negative A over B.

3x + 2y = 6

↓

$\displaystyle\ m = -\frac{3}{2}$

The slope cannot be simplified any more, so this would be the final answer.

- <em>Marlon Nunez</em>

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3 years ago

If xy + y² = 6, then the value of dy/dx at x= -1 is<br>

mylen [45]

Hi there!

$\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}$

$\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}$

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx) + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

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Thus, y = -2 and 3.

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2 years ago

Read 2 more answers