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2Find equations of all lines having slope 2 that are tangent to the curve y-x-6Select the correct choice below and fill in the answer box(es) within your choice.A. There are two lines tangent to the curve with a slope of 2. The equation of the line with the larger y-intercept isand the equation of the line with thesmaller y-intercept is(Type equations.)O B. There is only one line tangent to the curve with a slope of -2 and its equation is(Type an equation.)

Question

can you help me step by step please

2
Find equations of all lines having slope 2 that are tangent to the curve y
-
x-6
Select the correct choice below and fill in the answer box(es) within your choice.
A. There are two lines tangent to the curve with a slope of 2. The equation of the line with the larger y-intercept is
and the equation of the line with the
smaller y-intercept is
(Type equations.)
O B. There is only one line tangent to the curve with a slope of -2 and its equation is
(Type an equation.)
help_outline

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2 Find equations of all lines having slope 2 that are tangent to the curve y - x-6 Select the correct choice below and fill in the answer box(es) within your choice. A. There are two lines tangent to the curve with a slope of 2. The equation of the line with the larger y-intercept is and the equation of the line with the smaller y-intercept is (Type equations.) O B. There is only one line tangent to the curve with a slope of -2 and its equation is (Type an equation.)

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Step 1

Given information:

The equatio of the curve is

yx6)
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yx6)

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Step 2

Calculation:

Differentiate the function y with respect to x, we get

 

-2
y'=
(x-6)
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-2 y'= (x-6)

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Step 3

It is given that the slope is -2.

...

-2
-2
(x-6)2
1
=1
(x-6)2
(x-62=1
(x-7x-5) 0
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-2 -2 (x-6)2 1 =1 (x-6)2 (x-62=1 (x-7x-5) 0

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Math

Calculus

Derivative

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