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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:

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