Could you please help me??

Question

point-slope form linear equation
y-3 = 3(x+1)
what is the equation in standard form of a perpendicular line that passes through (5,1). i think you take 1/3 as slope, reciprocal, I am confused about how to proceed. I know you put variables on one side and constants on other side in standard form.

what is the x-intercept of the perpendicular line?
thanks

Answer 1

I assume the line is perpendicular to
the given line.

y-3 = 3(x+1).
y-3 = 3x+3,
-3x+y = 6,
3x-y = -6.

m1 = -A/B = -3/-1 = 3.

m2 = -1/3 = Negative reciprocal.
P(5,1).
y = mx + b,
y = (-1/3)*5 + b = 1,
b = 1 + 5/3 = 2 2/3 = 8/3.
y = (-1/3)x+8/3,
Convert to STD form:
x/3 + y = 8/3,
X + 3Y = 8.

Answer 2

ADDITION: Let Y = 0 to find X-int.
X + 3Y = 8,
X + 3*0 = 8,
X = 8 = x-int.

Answer 3

thank you so much for your help Henry, I really appreciate it. Ann

I understand now where I went wrong. first mistake i made was using positive 1/3 and then it was downhill from there.