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

First, remember that perpendicular lines have opposite and reciprocal slopes to the original line. That means for this line, your slope will be 2 (flip the fraction and change the sign). So we have:

[tex]y=2x+b[/tex]

Next, plug in the point that it passes through in order to find the y-intercept (b).

[tex]4=2(6)+b[/tex]

[tex]4=12+b[/tex]

[tex]b=-8[/tex]

So your equation will be:

[tex]y=2x-8[/tex]

Hope this helped!

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

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