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write an equation that passes through(1,4)and is perpendicular to the line y=-3x+1

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2 Answers

Alternate way of doing this using the point-slope formula.

Since y = -3x + 1 is in y=mx + b format, the slope is -3.

m = -3

The slope of the line perpendicular to y = -3x + 1 must be -(1/-3), or 1/3, since m1 = -1/m2.

Point - slope formula:

y - y1 = m (x - x1).

y - 4 = (1/3) (x - 1)

y - 4 = (1/3)x - 1/3

y = (1/3)x - 1/3 + 4

y = (1/3)x - 1/3 + 12/3

y = (1/3)x + 11/3

Comments

Hi Jehf;
y=-3x+1
The slope =-3
The perpendicular slope =1/3  Note that it is now a positive number.
y=(1/3)(x)+b
Obviously, the y-intercept has changed.  We must solve for it.
(1,4)
4=(1/3)(1)+b
4=1/3 + b
Let's subtract 1/3 from both sides...
(-1/3)+4=1/3 + b -1/3
3 2/3=b
 
y=(1/3)x+3 2/3

Comments