An equation of a line perpendicular to the line represented by the equation y=-1/2x-5 and passing through (6,-4)

We want to get an equation of a line perpendicular to the line represented by the equation y=-1/2x-5 and passing through (6,-4)

That equation is: y =2*x - 16

We know that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

A perpendicular line to the above shown must have a slope equal to the inverse of the opposite of the above slope, then a perpendicular line will be something like:

y = -(1/a)*x + c

Then for the line:

y=-1/2x-5

A general perpendicular line is written as:

y = 2*x + c

To find the value of c, we use the fact that this line must pass through (6, -4), we can replace the values of the point in the equation to get:

-4 = 2*6 + c

-4 = 12 + c

-4 - 12 = c = -16

Then the equation is:

y =2*x - 16

If you want to learn more, you can read:

link

y = 2x - 16

Step-by-step explanation:

Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes]:

-½ → 2

-4 = 2[6] + b

-16 = b

y = 2x - 16 >> Perpendicular Line in Slope-Intercept Form

I am joyous to assist you anytime.

452,489 to the nearest thousand is 452,000

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.