Answer:
y = -1/3x +5
Step-by-step explanation:
You want the slope-intercept equation of the line through (3, 4) that is perpendicular to y = 3x +2.
Perpendicular
The given line is in point-slope form, so we can read the slope as the coefficient of x: 3. The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/3
Equation
The point-slope equation is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -4 = -1/3(x -3) . . . . . perpendicular line through (3, 4)
We can solve for y and simplify to get the equation into slope-intercept form.
y = -1/3x +1 +4 . . . . . eliminate parentheses, add 4
y = -1/3x +5 . . . . perpendicular line through (3, 4)
