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

Solution:

Given, the equation of the line is y = -1/2 x - 5 ------------ (1)

The equation of the line in slope-intercept form is y = mx + c ----------------- (2)

Comparing (1) and (2),

m = -1/2

Slope of the line is -1/2.

Slope of the perpendicular line = -1/(-1/2)

= 1/(1/2)

= 2

Next, find the value of c by using the point (6,-4)

-4 = (2)(6) + c

-4 = 12 + c

0n solving,

c = -12 - 4

c = -16

Put the value of c and slope of perpendicular in (2) we get,

y = 2x - 16

Therefore, the equation of the line is y = 2x - 16.

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

Summary:

The equation of the line that passes through the point (6, -4) and is perpendicular to the line y = -1/2 x - 5 is y = 2x - 16.