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Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2

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Answer:

y = -1/3x +6

Explanation:

You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.

Slope-intercept form

The slope-intercept form of the equation of a line is ...

y = mx +b

where m is the slope, and b is the y-intercept.

Comparing this to the given equation, we see that m=3 for the given line.

Perpendicular lines

The slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...

desired slope = -1/m = -1/3

Y-intercept

The slope-intercept equation above can be solved for b to give ...

b = y -mx

Then the y-intercept for the line we want is ...

b = 5 -(-1/3)(3) = 5 +1 = 6

The equation of the desired line is y = -1/3x +6.

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Additional comment

Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.

Given slope = 3; perpendicular slope = -1/3

Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m

y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3

The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.

Find the equation of the straight line passing through the point (3,5) which is perpendicular-example-1
User John Cartwright
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