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What is the equation of the line that is perpendicular to a line with a slope of 2 and intersects that line at (4,2)?

User Amit Baderia
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1 Answer

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23 votes

Answer:

y = (-1/2) x + 4

Explanation:

Given line has slope 2 so the perpendicular line has the slope is -1/2 because ⊥ lines have their slopes negative reciprocal.

Both lines intersect at (4, 2) so this point belongs to both lines.

→general equation of a line y = mx+b where m = slope, b = y-intercept

→the equation for the line that has slope m = -1/2, is y = (-1/2) x+ b ( we do not know b now but will find it)

→we know that the point ( 4, 2) belongs to this line so the equation works for (x= 4, y= 2), substitute those values in the equation y = (-1/2) x+ b

2 = (-1/2)*4+ b which gives us b = 2+ (1/2)*4= 2+ 4/2 = 2+ 2 = 4

The equation of the line that is perpendicular to a line with a slope of 2 and intersects that line at (4,2) is y = (-1/2) x + 4

User Topgun
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