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3 years ago

what is the slope intercept form of a line that is perpendicular to y = x + 3 and passes through point (2, -4)

Mathematics

1 answer:

Assoli18 [71]3 years ago

3 0

Answer:

The equation of the perpendicular line is y = -x - 2

Step-by-step explanation:

* Lets revise the form of the slope intercept for

- The slope intercept form is y = mx + b, where m is the slope of

the line and b is the y-intercept

* Now lets revise the relation between the slopes of the

perpendicular lines

- If two lines are perpendicular, then the product of their slopes is -1

# Ex: If line L has slope m1 and line K has slope m2, and L ⊥ K

∴ m1 × m2 = -1

∴ m2 = -1/m1

* Now lets solve the problem

- We need to find the equation of the line which is perpendicular to

the line whose equation is y = x + 3 and passes through point (2 , -4)

- Find the slope of the given equation

∵ y = x + 3

- In this form the slope is the coefficient of x

∴ m = 1

- Find the slope of the perpendicular line

∵ The slope of the perpendicular line = -1/m

∴ The slope of it = -1/1 = -1

- Write the equation of the line with the value of the slope

∴ y = -x + b

- To find the value of b substitute x , y in the equation by the x and

y of the given point

∵ The line passes through point (2 , -4)

∵ y = -x + b

∴ -4 = -1(2) + b

∴ -4 = -2 + b ⇒ add 2 for both sides

∴ b = -2

- Write the equation with the value of b

∴ y = -x - 2

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Answer:

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Step-by-step explanation:

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4 years ago

Which choice is equivalent to the expression below when y2 0?<br> √y^2 + √16y^3 – 4y√y

DanielleElmas [232]

Answer:

Option C.

Step-by-step explanation:

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where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers)

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

$\sqrt{16*y^3} = \sqrt{16} \sqrt{y^3} = 4*\sqrt{y^3}$

And:

$y*\sqrt{y} = \sqrt{y^2} *\sqrt{y} = \sqrt{y^2*y} = \sqrt{y^3}$

If we apply these two to our initial expression, we can rewrite it as:

$\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}$

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Here we can use the second simplification again, to rewrite:

$\sqrt{y^3} = y*\sqrt{y}$

So, concluding, we have:

$\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y} = y*\sqrt{y}$

Then the correct option is C.

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