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
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