What is the equation of the line that is perpendicular to y = -4x +5 and passes through the point (4, -3)?

The slope of the line

y

=

−

1

2

x

−

5

is

m

1

=

−

1

2

(

y

=

m

x

+

c

)

The equation of the line passing through

(

6

,

−

4

)

is

y

−

y

1

=

m

(

x

−

x

1

)

or

y

+

4

=

m

(

x

−

6

)

. The product of

slopes of two perpendicular lines is

−

1

∴

m

⋅

m

1

=

−

1

or

m

⋅

(

−

1

2

)

=

−

1

∴

m

=

2

Therefore , the equation of the line is

y

+

4

=

2

(

x

−

6

)

or

2

x

−

y

−

16

=

0

[Ans]

Step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)