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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