Question

How do I write the equation of the line in standard form given this info:

Perpendicular to 3x - 1y = 4 with an x-intercept of 12 ?

Thanks! :)

Answer 1

-y=4-3x Multiply with(-1)

y=3x+4 (Slope=3)
Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 3, you can find the perpendicular slope by this formula:

mp=(-1)/m

where:
m-slope of line y=3x+4
mp is the perpendicular slope

mp=(-1/3)

So now we know the slope of the unknown line is (-1/3) its the negative reciprocal of 3 from the line y=3x+4
Also since the unknown line goes through (12,0), we can find the equation by plugging in this info into the point-slope formula.

Point-Slope Formula:

y-y1=mp(x-x1)
where mp is the slope and (x1,y1) is the given point.

mp=(-1/3)
x1=12
y1=0

y-0=(-1/3)*(x-12)
y=(-1/3)*x+(-1/3)*(-12)

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

So the equation of the line that is perpendicular to y=3x+4 and goes through (12,0) is:

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