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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: The correct option is triangle GDC

Step-by-step explanation: Please refer to the picture attached for further details.

The dimensions give for the cube are such that the top surface has vertices GBCF while the bottom surface has vertices HADE.

A right angle can be formed in quite a number of ways since the cube has right angles on all six surfaces. However the question states that the diagonal that forms the right angle runs "through the interior."

Therefore option 1 is not correct since the diagonal formed in triangle BDH passes through two surfaces. Triangle DCB is also formed with its diagonal passing only along one of the surfaces. Triangle GHE is also formed with its diagonal running through one of the surfaces.

However, triangle GDC is formed with its diagonal passing through the interior as shown by the "zigzag" line from point G to point D. And then you have another line running from vertex D to vertex C.