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Answer:
(a) y = -1/3x +10
(b) x +3y = 30
Step-by-step explanation:
The equation of the given line is in standard form, so it is convenient to start solving this problem by writing the perpendicular line in standard form. That is accomplished by swapping the x- and y-coefficients and negating one of them.
A straight swap would give -x+3y=constant. Standard form requires the leading coefficient be positive, so it is convenient to negate that one. The constant is found using the given point values. (x, y) = (12, 6)
x +3y = constant = (12) +3(6) = 30
The equation of the perpendicular line in standard form is ...
x +3y = 30
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Solving for y will give us the slope-intercept form.
3y = -x +30 . . . . . . subtract x
y = -1/3x +10 . . . . . divide by 3
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The desired equations are ...
(a) slope-intercept form: y = -1/3x +10
(b) standard form: x +3y = 30
