Write an equation of the line in slope-intercept form that passes through (-3,5) and is perpendicular to y = -3x- 1

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  y = 1/3x +6

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the opposite reciprocal of that:

  -1/(-3) = 1/3

The point-slope equation is then ...

  y -k = m(x -h) . . . . . for line of slope m through point (h, k)

Here, we have m = 1/3, (h, k) = (-3, 5), so the point-slope equation is ...

  y -5 = 1/3(x +3)

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

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