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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

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

5 votes

Answer:

y = -1/3x +6

Explanation:

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

Perpendicular line

The given equation is in slope-intercept form. This lets us identify its slope as 3.

y = mx + b . . . . . . line with slope m and y-intercept b

y = 3x +2 . . . . . . . line with slope 3 and y-intercept 2

The perpendicular line will have a slope that is the opposite reciprocal of this:

m = -1/3 . . . . slope of the perpendicular line

Point-slope form

The equation for a line with slope m through point (h, k) is ...

y -k = m(x -h)

The equation for a line with slope -1/3 through point (3, 5) is ...

y -5 = -1/3(x -3)

Slope-intercept form

Solving for y gives us ...

y = -1/3x +1 +5 . . . . . eliminate parentheses, add 5

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

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User Oleksii Moiseenko
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5.0k points