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What is the equation of a line perpendicular to y=2x-6 that passes through (5,4)?

User Abkds
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2 Answers

7 votes

Answer:


y = -(1)/(2)x + (13)/(2) \;\; \text{or}\\\\y = -0.5x + 6.5\\\\

Explanation:

The slope-intercept form of a straight line is

y = mx + b

where m = slope and b = y-intercept

A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through

Given
Line 1: y = 2x - 6
Slope m = 2

Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5

So the equation would be y = (-1/2)x + b

We can solve for b given the info that the line passes through (5,4)

Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b

4 = -5/2 + b

4 + 5/2 = b

8/2 + 5/2 = b

13/2 = b

or b = 13/2

So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2

or
y = -0.5x + 6.5


1 vote
your answer will be -0.5x+4.5
User MildlySerious
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3.7k points